A381147 E.g.f. A(x) satisfies A(x) = exp( sinh(x * A(x)) / A(x) ).

1, 1, 1, 2, 13, 92, 621, 5112, 56057, 705168, 9480665, 141039648, 2366242693, 43609330624, 864164283269, 18414385180544, 422574196387953, 10374625080684800, 270563138370828465, 7472794772378583552, 218190569313134267517, 6714970997524417977344

Offset: 0

Author

Seiichi Manyama, Feb 15 2025

Keywords

• nonn

Crossrefs

Cf. A003724, A162650, A219503.

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-k+1)^(k-1)*a136630(n, k));

Formula

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