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

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.

Cf. A270386, A371518.

Sequence in context: A371584 A288950 A005415 * A219868 A224885 A371575

Adjacent sequences: A371520 A371521 A371522 * A371524 A371525 A371526

Keyword

nonn

Author

Seiichi Manyama, Mar 26 2024

Status

approved