A375612 - OEIS

A375612

Triangle read by rows: T(n, k) = n! * 4^k * hypergeom([-k], [-n], -1/4).

1, 1, 3, 2, 7, 25, 6, 22, 81, 299, 24, 90, 338, 1271, 4785, 120, 456, 1734, 6598, 25121, 95699, 720, 2760, 10584, 40602, 155810, 598119, 2296777, 5040, 19440, 75000, 289416, 1117062, 4312438, 16651633, 64309755, 40320, 156240, 605520, 2347080, 9098904, 35278554, 136801778, 530555479, 2057912161

(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} (-4)^(k - j)*binomial(k, k - j)*(n - j)!.

EXAMPLE

Triangle starts:

[0] 1;

[1] 1, 3;

[2] 2, 7, 25;

[3] 6, 22, 81, 299;

[4] 24, 90, 338, 1271, 4785;

[5] 120, 456, 1734, 6598, 25121, 95699;

[6] 720, 2760, 10584, 40602, 155810, 598119, 2296777;

[7] 5040, 19440, 75000, 289416, 1117062, 4312438, 16651633, 64309755;

...

MATHEMATICA

T[n_, k_] := (-1)^k*Sum[(-4)^(k - j)*Binomial[k, k - j]*(n - j)!, {j, 0, k}];

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

CROSSREFS

Cf. A375613, A000142, A001907 (main diagonal).

Cf. A374427, A374428, A375446, A375447, A375597, A375600.

Sequence in context: A111928 A348695 A248054 * A329421 A100985 A176802

Adjacent sequences: A375609 A375610 A375611 * A375613 A375614 A375615

KEYWORD

nonn,tabl

AUTHOR

Detlef Meya, Aug 21 2024

STATUS

approved