A371429 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 - x^4) ).

1, 3, 12, 55, 272, 1413, 7599, 41933, 236053, 1350093, 7822620, 45817390, 270815730, 1613300978, 9676131942, 58380176644, 354081959367, 2157570900137, 13201923181308, 81084900544971, 499711105642851, 3089163236655363, 19150916212748940, 119031956868317285

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3-x^4))/x)
(PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(n+1, k)*binomial(3*n-3*k+3, n-4*k))/(n+1);

Crossrefs

Cf. A107264, A127897, A371428.

Cf. A369159.

Sequence in context: A256142 A024038 A373960 * A361356 A007199 A179848

Adjacent sequences: A371426 A371427 A371428 * A371430 A371431 A371432

Keyword

nonn

Author

Seiichi Manyama, Mar 23 2024

Status

approved