The On-Line Encyclopedia of Integer Sequences (OEIS)

A225478 revision #8

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.

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

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OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..36.

Peter Luschny, Generalized Eulerian polynomials.

Peter Luschny, The Stirling-Frobenius numbers.

FORMULA

For a recurrence see the Sage program.

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.

EXAMPLE

[n\k][ 0, 1, 2, 3, 4, 5, 6 ]

[0] 1,