A371523 - OEIS

A371523

G.f. A(x) satisfies A(x) = (1 + x*A(x)^3 / (1-x))^2.

1, 2, 15, 142, 1533, 17924, 220936, 2827218, 37202580, 500228562, 6842899886, 94931338876, 1332438761910, 18887047322030, 269986427261981, 3887654399820062, 56337997080499605, 821021578186212094, 12024687038651388155, 176900548019426869808, 2612917215947948178941

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) = 2 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(6*k+1,k)/(5*k+2).

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A349333.

PROG

(PARI) a(n) = 2*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+1, k)/(5*k+2));

CROSSREFS

Cf. A349333, A371379, A371519, A371521, A371522.