A380093 E.g.f. A(x) satisfies A(x) = sqrt( 1 + 2*x*exp(x*A(x)) ).

1, 1, 1, 6, 13, 180, 501, 13720, 34777, 2014992, 2512585, 491642976, -564313947, 181714012480, -836832558275, 95473740036480, -856984734161999, 68029327826567424, -954950936641491951, 63368301861354866176, -1238053892876418633155, 74904417332353810338816

Offset: 0

Author

Seiichi Manyama, Jan 12 2025

Keywords

• sign

Crossrefs

Cf. A161631, A380094.

Cf. A380035, A380050.

Programs

PARI

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

Formula

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