A387452 Expansion of (1/x) * Series_Reversion( x / ((1+x)^4 * (x+(1+x)^2)) ).

1, 7, 68, 768, 9456, 123129, 1667453, 23246489, 331414377, 4809423412, 70807888135, 1055033018662, 15879182972235, 241062144838080, 3686889377884268, 56755774874179752, 878701543739263551, 13673314925210571263, 213733210946062067925, 3354567005999632187928

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..600

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(6*n-2*k+6,n-k).

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

Mathematica

Table[SeriesCoefficient[((1+x)^4*(x+(1+x)^2))^(n+1), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 18 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^4*(x+(1+x)^2)))/x)
(Magma) [1/(n+1)*&+[Binomial(n+1, k)*Binomial(6*n-2*k+6, n-k): k in [0..n]]: n in [0..35]]; // Vincenzo Librandi, Oct 18 2025

Crossrefs

Cf. A387427.

Sequence in context: A390334 A328046 A379521 * A371392 A306386 A136629

Adjacent sequences: A387449 A387450 A387451 * A387453 A387454 A387455

Keyword

nonn

Author

Seiichi Manyama, Sep 28 2025

Status

approved