A369301 - OEIS

A369301

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

1, 3, 15, 94, 657, 4902, 38236, 308025, 2542965, 21401780, 182934144, 1583745114, 13858675065, 122379042879, 1089156646584, 9759520978270, 87975115569873, 797233088237190, 7258632128721117, 66367727370376632, 609132332475784548, 5610015849998778144

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

Peter Bala, Fractional iteration of a series inversion operator

Index entries for reversions of series

FORMULA

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(4*n-3*k+2,n-3*k).

a(n) = (1/(n+1)) * [x^n] 1/( (1-x)^3 * (1-x^3)^3 )^(n+1). - Seiichi Manyama, Feb 14 2024

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3*(1-x^3)^3)/x)

(PARI) a(n, s=3, t=3, u=3) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);

CROSSREFS

Cf. A369299, A369300.

Cf. A369270.

Sequence in context: A243245 A128240 A369270 * A368964 A274734 A177341

Adjacent sequences: A369298 A369299 A369300 * A369302 A369303 A369304

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jan 18 2024

STATUS

approved