A392583 Expansion of 1 / ((1-x)^5 - x^2)^2.

1, 10, 57, 250, 958, 3422, 11759, 39416, 129700, 420542, 1347449, 4275770, 13460154, 42089400, 130860258, 404848066, 1247092849, 3826948536, 11704162210, 35687710162, 108522683624, 329199712980, 996399154254, 3009727674010, 9074343647823, 27312573390012

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-43,110,-191,232,-200,118,-45,10,-1).

Formula

a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(n+3*k+9,n-2*k).

a(n) = 10*a(n-1) - 43*a(n-2) + 110*a(n-3) - 191*a(n-4) + 232*a(n-5) - 200*a(n-6) + 118*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-x)^5-x^2)^2)

Crossrefs

Cf. A369803.

Sequence in context: A047780 A055251 A038733 * A004142 A006529 A337001

Adjacent sequences: A392580 A392581 A392582 * A392584 A392585 A392586

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 17 2026

Status

approved