A372138 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^2*(1 + 4*x*A(x))^(1/2) ).

1, 1, 5, 24, 149, 945, 6464, 45360, 328661, 2426971, 18244053, 138988092, 1071271988, 8336754044, 65421283160, 517081111568, 4112772482949, 32894217211791, 264391091936095, 2134466592084000, 17300375657257629, 140728012021470193, 1148477345709237844

Offset: 0

Author

Seiichi Manyama, Apr 20 2024

Keywords

• nonn

Crossrefs

Cf. A372136.

Programs

PARI

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

Formula

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