A383637 Expansion of 1/((1-x) * (1+3*x) * (1-5*x)).

1, 3, 22, 90, 511, 2373, 12412, 60420, 307021, 1520343, 7646002, 38097150, 190884331, 953225913, 4769716792, 23837822280, 119221396441, 596010127083, 2980341200782, 14900834307810, 74506786627351, 372526087871853, 1862653975153972, 9313199268385740, 46566208164081061

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (3,13,-15).

Formula

a(n) = Sum_{k=0..floor(n/2)} 16^k * binomial(n+2,2*k+2).

a(n) = (5^(n+2) + (-3)^(n+2) - 2)/32 = (A120612(n+2) - 1)/16.

a(n) = 3*a(n-1) + 13*a(n-2) - 15*a(n-3).

a(n) = Sum_{k=0..n} 4^k * (-3)^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).

a(n) = Sum_{k=0..n} (-4)^k * 5^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).

Prog

(PARI) a(n) = (5^(n+2)+(-3)^(n+2)-2)/32;

Crossrefs

Cf. A079773, A120612.

Sequence in context: A277228 A302272 A302723 * A095663 A254332 A009029

Adjacent sequences: A383634 A383635 A383636 * A383638 A383639 A383640

Keyword

nonn,easy

Author

Seiichi Manyama, May 03 2025

Status

approved