A375446 - OEIS

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A375446

Triangle read by rows: T(n, k) = n! * 3^k * hypergeom([-k], [-n], -1/3).

5

1, 1, 2, 2, 5, 13, 6, 16, 43, 116, 24, 66, 182, 503, 1393, 120, 336, 942, 2644, 7429, 20894, 720, 2040, 5784, 16410, 46586, 132329, 376093, 5040, 14400, 41160, 117696, 336678, 963448, 2758015, 7897952, 40320, 115920, 333360, 958920, 2759064, 7940514, 22858094, 65816267, 189550849

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..44.

FORMULA

T(n, k) = (-1)^k*Sum_{j=0..k} (-3)^(k - j)*binomial(k, k - j)*(n - j)!.

EXAMPLE

Triangle starts:

[0] 1,

[1] 1, 2,

[2] 2, 5, 13,

[3] 6, 16, 43, 116,

[4] 24, 66, 182, 503, 1393,

[5] 120, 336, 942, 2644, 7429, 20894,

[6] 720, 2040, 5784, 16410, 46586, 132329, 376093,

[7] 5040, 14400, 41160, 117696, 336678, 963448, 2758015, 7897952,

...

MATHEMATICA

T[n_, k_] := (-1)^k*Sum[(-3)^(k - j)*Binomial[k, k - j]*(n - j)!, {j, 0, k}];

Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

CROSSREFS

Cf. A375447, A000142, A000180 (diagonal).

Cf. A374427, A374428.

Sequence in context: A209218 A208322 A208175 * A078413 A019083 A355863

Adjacent sequences: A375443 A375444 A375445 * A375447 A375448 A375449

KEYWORD

nonn,tabl

AUTHOR

Detlef Meya, Aug 15 2024

STATUS

approved