A389372 Expansion of g/(1 + x^3*g), where g = 1+x*g^4 is the g.f. of A002293.

1, 1, 4, 21, 138, 960, 7033, 53483, 418353, 3344640, 27208776, 224505153, 1874386555, 15805523788, 134415742850, 1151553504819, 9929027280310, 86096574522884, 750318332572729, 6568311432066472, 57731592862206081, 509279853747972748, 4507516441681769525

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (k+1) * binomial(4*n-11*k+1,n-3*k)/(4*n-11*k+1).

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*(k+1)*binomial(4*n-11*k+1, n-3*k)/(4*n-11*k+1));

Crossrefs

Cf. A391324, A391326.

Cf. A002293, A390298.

Sequence in context: A391324 A369784 A121124 * A180399 A384264 A349534

Adjacent sequences: A389369 A389370 A389371 * A389373 A389374 A389375

Keyword

nonn

Author

Seiichi Manyama, Dec 07 2025

Status

approved