A369444 Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x^4)) ).

1, 1, 1, 1, 2, 7, 22, 57, 131, 298, 738, 2003, 5600, 15380, 41224, 109769, 296009, 813315, 2261647, 6305930, 17554044, 48851034, 136350556, 382408995, 1077164245, 3042452536, 8606495236, 24377127256, 69159381856, 196600128592, 559990599808, 1597797525833

Offset

0,5

Links

Table of n, a(n) for n=0..31.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x^4)))/x)
(PARI) a(n, s=4, t=1, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial(u*(n+1), n-s*k))/(n+1);

Crossrefs

Cf. A036765, A198951.

Sequence in context: A212384 A306347 A351969 * A371716 A063019 A369845

Adjacent sequences: A369441 A369442 A369443 * A369445 A369446 A369447

Keyword

nonn

Author

Seiichi Manyama, Jan 23 2024

Status

approved