The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A225478

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A225478

Triangle read by rows, 4^k*s_4(n, k) where s_m(n, k) are the Stirling-Frobenius cycle numbers of order m; n >= 0, k >= 0.
(history; published version)

#17 by Peter Luschny at Fri Aug 02 13:45:33 EDT 2019

STATUS

proposed

approved

#16 by Jean-François Alcover at Fri Aug 02 11:54:04 EDT 2019

STATUS

editing

proposed

#15 by Jean-François Alcover at Fri Aug 02 11:53:45 EDT 2019

DATA

1, 3, 4, 21, 40, 16, 231, 524, 336, 64, 3465, 8784, 7136, 2304, 256, 65835, 180756, 170720, 72320, 14080, 1024, 1514205, 4420728, 4649584, 2346240, 613120, 79872, 4096, 40883535, 125416476, 143221680, 81946816, 25939200, 4609024, 430080, 16384, 1267389585, 4051444896, 4941537984, 3113238016, 1131902464, 246636544, 31768576, 2228224, 65536

MATHEMATICA

s[_][0, 0] = 1; s[m_][n_, k_] /; (k > n || k < 0) = 0; s[m_][n_, k_] := s[m][n, k] = s[m][n - 1, k - 1] + (m*n - 1)*s[m][n - 1, k];

T[n_, k_] := 4^k*s[4][n, k];

Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 02 2019 *)

STATUS

approved

editing

Discussion

Fri Aug 02

11:54

Jean-François Alcover: Completed last row of data.

#14 by Peter Luschny at Fri Aug 07 04:01:32 EDT 2015

STATUS

editing

approved

#13 by Peter Luschny at Fri Aug 07 04:01:14 EDT 2015

FORMULA

For a recurrence see the Sage program.

For a recurrence see the Sage program.T(n,k) = 4^k * A225471(n,k). - Philippe Deléham, May 14 2015.

#12 by Peter Luschny at Fri Aug 07 03:59:26 EDT 2015

FORMULA

For a recurrence see the Sage program.T(n,k) = 4^k * A225471(n,k). - _Philippe Deléham_, May 14 2015.

T(n, 0) ~ A008545; T(n, n) ~ A000302; T(n, n-1) ~ A002700.

row sums ~ A034176; alternating row sums ~ A008545.

T(n,k) = 4^k * A225471(n,k). - Philippe Deléham, May 14 2015.

CROSSREFS

T(n, 0) ~ A008545; T(n, n) ~ A000302; T(n, n-1) ~ A002700.

row sums ~ A034176; alternating row sums ~ A008545.

Cf. A225471, A132393 (m=1), A028338 (m=2), A225477 (m=3).

STATUS

approved

editing

#11 by Alois P. Heinz at Fri May 15 14:49:08 EDT 2015

STATUS

editing

approved

#10 by Alois P. Heinz at Fri May 15 14:48:54 EDT 2015

COMMENTS

Triangle T(n,k), read by rows, given by (3, 4, 7, 8, 11, 12, 15, 16, ... (A014601)) DELTA (4, 0, 4, 0, 4, 0, 4, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, May 14 2015.

#9 by Alois P. Heinz at Thu May 14 21:43:27 EDT 2015

COMMENTS

Triangle T(n,k), read by rows, given by (3, 4, 7, 8, 11, 12, 15, 16, ...) DELTA (4, 0, 4, 0, 4, 0, 4, 0, ...) where DELTA is the operator defined in A084938. _- _Philippe Deléham_, May 14 2015.

FORMULA

T(n,k) = 4^k * A225471(n,k). _- _Philippe Deléham_, May 14 2015.

STATUS

proposed

editing

Discussion

Thu May 14

21:44

Alois P. Heinz: What is 3, 4, 7, 8, 11, 12, 15, 16, ...? 
OEIS lists 9 sequences.

22:26

Philippe Deléham: Partial sums of : 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, ...

#8 by Philippe Deléham at Thu May 14 19:02:11 EDT 2015

STATUS

editing

proposed