A376328 G.f. satisfies A(x) = (1 + x*A(x)*(1 + x*A(x)))^5.

1, 5, 40, 380, 3970, 44051, 509575, 6077435, 74194780, 922644310, 11646083631, 148827827450, 1921724362880, 25034267112600, 328614891689845, 4342322118727300, 57715241768897445, 771087466276360970, 10349495416322497575, 139486475071720234920, 1886980259513934080860, 25613816043115261657425

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)^5 ).

G.f.: B(x)^5, where B(x) is the g.f. of A365189.

Prog

(PARI) a(n, s=1, t=5) = 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)^5)/x)

Crossrefs

Cf. A143927, A365128, A376320.

Cf. A365189.

Sequence in context: A359984 A271957 A220673 * A369125 A130564 A368011

Adjacent sequences: A376325 A376326 A376327 * A376329 A376330 A376331

Keyword

nonn

Author

Seiichi Manyama, Sep 20 2024

Status

approved