A365084 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x)^5.

1, 1, -4, 6, 6, -49, 95, 24, -592, 1417, -414, -6809, 20142, -14831, -73353, 274761, -311105, -715647, 3607624, -5463428, -5785294, 45588556, -87189477, -25565196, 552659892, -1305250324, 340413165, 6379267117, -18606431142, 13202513476, 69064770845

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (-4,-10,-10,-5,-1).

Formula

G.f.: A(x) = 1/( 1 - x/(1+x)^5 ).

a(n) = -4*a(n-1) - 10*a(n-2) - 10*a(n-3) - 5*a(n-4) - a(n-5) for n > 5.

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n+4*k-1,n-k).

Mathematica

LinearRecurrence[{-4, -10, -10, -5, -1}, {1, 1, -4, 6, 6, -49}, 1 + 30] (* Robert P. P. McKone, Aug 21 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n+4*k-1, n-k));

Crossrefs

Cf. A106510, A127896, A365083.

Cf. A079675.

Sequence in context: A295512 A064214 A019203 * A082237 A348958 A348348

Adjacent sequences: A365081 A365082 A365083 * A365085 A365086 A365087

Keyword

sign,easy

Author

Seiichi Manyama, Aug 21 2023

Status

approved