A380050 E.g.f. A(x) satisfies A(x) = sqrt( 1 + 2*x*exp(x)*A(x) ).

1, 1, 3, 9, 25, 25, -429, -4151, -8175, 320625, 5241475, 23329801, -705579159, -18521117303, -150119840493, 3366485315145, 138253031778721, 1780881865542625, -28047359274759549, -1854674541474191351, -34985197604145203655, 332608115115937927161

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

E.g.f.: exp( arcsinh(x*exp(x)) ).

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

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(asinh(x*exp(x)))))
(PARI) a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(k/2+1/2, k)/((k+1)*(n-k)!));

Crossrefs

Cf. A006153, A380051.

Cf. A297010, A380044.

Sequence in context: A148920 A351937 A204448 * A032681 A293852 A005209

Adjacent sequences: A380047 A380048 A380049 * A380051 A380052 A380053

Keyword

sign

Author

Seiichi Manyama, Jan 11 2025

Status

approved