A387734 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x^3*(1+x))) ).

1, 2, 5, 15, 53, 210, 887, 3873, 17250, 78002, 357448, 1657812, 7770608, 36757528, 175245503, 841182458, 4061644614, 19714293204, 96135001449, 470756344587, 2313922229276, 11412665170566, 56464944628087, 280161701003495, 1393719256942099, 6950069112139172

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(2*n+k+2,n-3*k).

a(n) = (1/(n+1)) * [x^n] ((1+x)^2 * (1+x^3*(1+x)))^(n+1).

Mathematica

Table[SeriesCoefficient[((1+x)^2*(1+x^3*(1+x)))^(n+1), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 20 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+x^3*(1+x))))/x)
(Magma) [1/(n+1)*&+[Binomial(n+1, k)*Binomial(2*n+k+2, n-3*k): k in [0..Floor(n/3)]]: n in [0..35]]; // Vincenzo Librandi, Oct 20 2025

Crossrefs

Cf. A369443, A387774, A387777.

Sequence in context: A107589 A249892 A352853 * A387669 A006790 A007548

Adjacent sequences: A387731 A387732 A387733 * A387735 A387736 A387737

Keyword

nonn

Author

Seiichi Manyama, Oct 07 2025

Status

approved