A388731 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (x+(1+x)^4)) ).

1, 7, 66, 721, 8580, 107953, 1412460, 19024180, 262019905, 3673362220, 52246391527, 752042248866, 10934636711988, 160363034183879, 2369374773397603, 35235601933270018, 527000145778973719, 7922106771908157083, 119628952546666603571, 1813836377151137349917

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(6*n-4*k+6,n-k).

a(n) = (1/(n+1)) * [x^n] ((1+x)^2 * (x+(1+x)^4))^(n+1).

Mathematica

Table[(1/(n+1)) Coefficient[((1+x)^2*(x+(1+x)^4))^(n+1), x, n], {n, 0, 19}] (* Vincenzo Librandi, Sep 30 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(x+(1+x)^4)))/x)
(Magma) R<x> := PolynomialRing(Rationals()); [ (1/(n+1))*Coefficient((((1+x)^2* (x+(1+x)^4))^(n+1)), n) : n in [0..30] ]; // Vincenzo Librandi, Sep 30 2025

Crossrefs

Cf. A003168, A364792, A365192.

Cf. A364748, A378685, A388732.

Cf. A388727.

Sequence in context: A394270 A371780 A065097 * A300991 A122705 A185181

Adjacent sequences: A388728 A388729 A388730 * A388732 A388733 A388734

Keyword

nonn

Author

Seiichi Manyama, Sep 20 2025

Status

approved