A372463 - OEIS

A372463

Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x+x^3)^2 )^n.

1, 3, 21, 159, 1261, 10268, 85065, 713345, 6036381, 51438741, 440780736, 3794261496, 32784723361, 284184613586, 2470101750095, 21520640950334, 187885215032925, 1643315666085399, 14396340879235851, 126302446713155886, 1109524512806397656

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n+k-1,k) * binomial(4*n-2*k-1,n-3*k).

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x) * (1-x+x^3)^2 ). See A368974.

PROG

(PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, (-1)^k*binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k));

CROSSREFS

Cf. A368974, A372459.

Sequence in context: A205773 A192364 A286918 * A358953 A189508 A074570

Adjacent sequences: A372460 A372461 A372462 * A372464 A372465 A372466

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 01 2024

STATUS

approved