A371319 E.g.f. satisfies A(x) = exp(x) + x^2*A(x)^2.

1, 1, 3, 13, 97, 881, 10561, 147505, 2453025, 46234081, 988356961, 23439248801, 613770379729, 17541180307249, 544252239627825, 18203134190836561, 653255126565875521, 25031281492493722817, 1020214630056827123137, 44067538801695759773761

Offset: 0

Author

Seiichi Manyama, Mar 18 2024

Keywords

• nonn

Crossrefs

Cf. A087208, A371320.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(2*exp(x)/(1+sqrt(1-4*x^2*exp(x)))))

PARI

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

Formula

E.g.f.: 2*exp(x)/(1 + sqrt(1 - 4*x^2*exp(x))).

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