A381784 G.f. A(x) satisfies A(x) = (1 + x*A(x)^4) * C(x*A(x)^2), where C(x) is the g.f. of A000108.

1, 2, 15, 153, 1799, 22969, 309479, 4331175, 62349575, 917335467, 13732751589, 208509835114, 3203279694575, 49701110565986, 777708690091907, 12258870836704797, 194475105262057575, 3102607480658510165, 49746656826517452788, 801205735002960886531, 12956005807148939155717

Offset

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A234461, A381774.

Cf. A000108.

Sequence in context: A002103 A191364 A308379 * A373357 A233832 A185756

Adjacent sequences: A381781 A381782 A381783 * A381785 A381786 A381787

Keyword

nonn

Author

Seiichi Manyama, Mar 07 2025

Status

approved