A372416 Coefficient of x^n in the expansion of ( (1-x+x^3) / (1-x) )^(2*n).

1, 0, 0, 6, 8, 10, 78, 196, 376, 1446, 4390, 10648, 32822, 101426, 276976, 808666, 2449528, 7046942, 20491458, 61124482, 179376718, 525065722, 1556298700, 4598892274, 13546834582, 40109057710, 118836735758, 351539306142, 1041872654824, 3091535558296

Offset

0,4

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(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)^2 / (1-x+x^3)^2 ). See A372418.

Prog

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

Crossrefs

Cf. A372417, A372418.

Sequence in context: A145749 A235599 A242778 * A184113 A309627 A085412

Adjacent sequences: A372413 A372414 A372415 * A372417 A372418 A372419

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved