A381938 G.f. A(x) satisfies A(x) = (1 + x)^2 * B(x*A(x)), where B(x) is the g.f. of A001764.

1, 3, 9, 52, 380, 3066, 26304, 235314, 2170312, 20487963, 196988392, 1922327792, 18990571724, 189548947601, 1908604524752, 19364096602370, 197761735366804, 2031444188437719, 20974821788118024, 217561484977675026, 2265961977605950416, 23688432825547509283

Offset: 0

Author

Seiichi Manyama, Mar 10 2025

Keywords

• nonn

Crossrefs

Cf. A366694, A367640, A381941.

Cf. A001764, A381785.

Programs

PARI

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

Formula

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

a(n) = A381785(n) + A381785(n-1).