A381309 E.g.f. A(x) satisfies A(x) = exp( sinh(x * A(x)^(1/2)) / A(x)^(1/2) ).

1, 1, 1, 2, 9, 42, 209, 1381, 11121, 96744, 936337, 10323865, 125245457, 1640739336, 23339285601, 359236548033, 5918755368865, 103922094286976, 1941594484205793, 38448924176712705, 803753373207738337, 17693469280066921736, 409266060724837855057, 9922356658347766201841

Offset: 0

Author

Seiichi Manyama, Feb 19 2025

Keywords

• nonn

Crossrefs

Cf. A136630.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (n/2-k/2+1)^(k-1)*a136630(n, k));

Formula

a(n) = Sum_{k=0..n} (n/2-k/2+1)^(k-1) * A136630(n,k).