A381262 Expansion of e.g.f. exp( -LambertW(-2 * sinh(x)) / 2 ).

1, 1, 5, 50, 749, 15132, 385953, 11907520, 431376345, 17954558928, 844397935517, 44287052219104, 2563077440429701, 162259043437047104, 11154216390820950585, 827464985582299977728, 65889383717510410496689, 5605511011776107945980160, 507429545895353798767136181

Offset: 0

Author

Seiichi Manyama, Feb 18 2025

Keywords

• nonn

Crossrefs

Cf. A136630, A219503.

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

Formula

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

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