A365764 Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1+x) ).

1, 4, 25, 188, 1563, 13840, 127972, 1221260, 11938471, 118936100, 1203155633, 12325599632, 127611357300, 1333153669632, 14035828918560, 148773617605036, 1586305110768863, 17002975960876300, 183102052226442475, 1980078493171083292, 21493846031259095539

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..940

Formula

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

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+1, k)*binomial(4*n-k+2, n-k))/(n+1);

Crossrefs

Cf. A003169, A006318, A365765, A365766.

Cf. A365751.

Sequence in context: A369479 A166697 A054368 * A135147 A221382 A215791

Adjacent sequences: A365761 A365762 A365763 * A365765 A365766 A365767

Keyword

nonn

Author

Seiichi Manyama, Sep 18 2023

Status

approved