A375363 Expansion of 1/( (1 + x)^2 * (1 - x*(1 + x)^3) ).

1, -1, 5, 1, 19, 30, 102, 242, 666, 1718, 4555, 11937, 31435, 82615, 217301, 571372, 1502572, 3951188, 10390340, 27322972, 71850149, 188941251, 496850977, 1306548125, 3435774983, 9034913514, 23758733842, 62477347430, 164294064510, 432037221810

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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

Formula

a(n) = -a(n-1) + 4*a(n-2) + 10*a(n-3) + 10*a(n-4) + 5*a(n-5) + a(n-6).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/((1+x)^2*(1-x*(1+x)^3)))
(PARI) a(n) = sum(k=0, n, binomial(3*k-2, n-k));

Crossrefs

Cf. A375362.

Sequence in context: A286232 A147437 A147369 * A066480 A136394 A145372

Adjacent sequences: A375359 A375360 A375362 * A375364 A375365 A375366

Keyword

sign

Author

Seiichi Manyama, Aug 13 2024

Status

approved