A365843 - OEIS

A365843

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

1, 6, 54, 578, 6810, 85278, 1113854, 15004746, 206955378, 2908113974, 41484917958, 599202514578, 8745727050762, 128790559374030, 1911191826600462, 28551332345784730, 429040549473424866, 6480799118506040934, 98349636147075506006, 1498732955394826784226

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

FORMULA

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

G.f.: B^3, where B is the g.f. of A144097.

PROG

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

CROSSREFS

Cf. A007297, A365842, A365844, A365845.