A372377 Expansion of (1/x) * Series_Reversion( x * (1+x)^2 / (1+x+x^3)^3 ).

1, 1, 1, 4, 13, 31, 91, 313, 988, 3095, 10377, 35146, 117682, 400117, 1381582, 4779997, 16599766, 58095076, 204319835, 720756820, 2552544940, 9074710255, 32356325145, 115679362789, 414701335849, 1490297002000, 5367227015647, 19369656905210, 70038419041844

Offset

0,4

Links

Table of n, a(n) for n=0..28.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1+x)^2/(1+x+x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=-2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);

Crossrefs

Cf. A372376, A372378.

Sequence in context: A027998 A367010 A026567 * A218958 A226839 A270976

Adjacent sequences: A372374 A372375 A372376 * A372378 A372379 A372380

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved