A376320 G.f. satisfies A(x) = (1 + x*A(x)*(1 + x*A(x)))^4.

1, 4, 26, 200, 1691, 15180, 142038, 1370076, 13526645, 136024876, 1388394234, 14346699052, 149790104030, 1577765967600, 16745718467070, 178912981116840, 1922688816819276, 20769064846817136, 225384498769815750, 2455985319885345820, 26862562977746930145, 294807644917408047060

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for reversions of series

Formula

If g.f. satisfies A(x) = (1 + x*A(x)*(1 + x*A(x))^s)^t, then a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(t*(n+1),k) * binomial(s*k,n-k).

G.f.: (1/x) * Series_Reversion( x / (1+x+x^2)^4 ).

G.f.: B(x)^4, where B(x) is the g.f. of A365183.

Prog

(PARI) a(n, s=1, t=4) = sum(k=0, n, binomial(t*(n+1), k)*binomial(s*k, n-k))/(n+1);
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^2)^4)/x)

Crossrefs

Cf. A143927, A365128, A376328.

Cf. A365183.

Sequence in context: A278393 A349361 A192499 * A271935 A246509 A369107

Adjacent sequences: A376317 A376318 A376319 * A376321 A376322 A376323

Keyword

nonn

Author

Seiichi Manyama, Sep 20 2024

Status

approved