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
Keywords
Programs
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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)!));
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)! ).