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A387498

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

1, 2, 6, 25, 122, 632, 3384, 18623, 104920, 602483, 3512908, 20739996, 123733367, 744784393, 4517612643, 27586215057, 169444441944, 1046218599080, 6489822123269, 40425135509230, 252756257488136, 1585740652179357, 9979540881991656, 62982847279132601

(list; graph; refs; listen; history; text; internal format)

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/2)} binomial(n+1,k) * binomial(2*n+3*k+2,n-2*k).

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

MATHEMATICA

Table[SeriesCoefficient[((1+x)^2*(1+x^2*(1+x)^3))^(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^2*(1+x)^3)))/x)

(Magma) [1/(n+1)*&+[Binomial(n+1, k)*Binomial(2*n+3*k+2, n-2*k): k in [0..Floor(n/2)]]: n in [0..35]]; // Vincenzo Librandi, Oct 20 2025

CROSSREFS

Cf. A369439, A387496, A387497.

Sequence in context: A391299 A321720 A358499 * A357949 A387668 A321186

Adjacent sequences: A387495 A387496 A387497 * A387499 A387500 A387501

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 06 2025

STATUS

approved

URL: https://oeis.org/A387498

⇱ A387498 - OEIS