A381853 Expansion of 1/( Product_{k=0..3} (1 + (-1)^k * (2*k+1) * x) ).

1, 4, 50, 260, 2331, 13944, 110020, 709720, 5275061, 35405084, 255481590, 1750273980, 12442802191, 86146389424, 607794442760, 4230723277040, 29734284335721, 207543980222964, 1455788202761530, 10175616585022900, 71303822881787651, 498754234084641704

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (4,34,-76,-105).

Formula

a(n) = Sum_{k=0..n} 4^k * (-5)^(n-k) * binomial(n+3,k+3) * Stirling2(k+3,3).

a(n) = Sum_{k=0..n} (-4)^k * 7^(n-k) * binomial(n+3,k+3) * Stirling2(k+3,3).

a(n) = (7^(n+3) - 3*3^(n+3) + 3*(-1)^(n+3) - (-5)^(n+3))/384.

a(n) = 4*a(n-1) + 34*a(n-2) - 76*a(n-3) - 105*a(n-4).

G.f.: B(x)^4, where B(x) is the g.f. of A383624.

Prog

(PARI) a(n) = (7^(n+3)-3*3^(n+3)+3*(-1)^(n+3)-(-5)^(n+3))/384;

Crossrefs

Cf. A383624.

Sequence in context: A189894 A275291 A240396 * A197473 A219566 A202790

Adjacent sequences: A381850 A381851 A381852 * A381854 A381855 A381856

Keyword

nonn,easy

Author

Seiichi Manyama, May 03 2025

Status

approved