A368931 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x-x^3) ).

1, 2, 7, 31, 154, 819, 4560, 26244, 154874, 932074, 5698745, 35297535, 221016593, 1396717756, 8896798020, 57062237502, 368201804973, 2388587515239, 15568995139404, 101913055166811, 669678357109300, 4415837460391845, 29210203356645090

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

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

Crossrefs

Cf. A236339, A368932, A368933.

Cf. A049140, A054514.

Sequence in context: A369297 A256672 A366052 * A007863 A369214 A302061

Adjacent sequences: A368928 A368929 A368930 * A368932 A368933 A368934

Keyword

nonn

Author

Seiichi Manyama, Jan 10 2024

Status

approved