A380046 E.g.f. A(x) satisfies A(x) = 1 + 2*x*exp(x)*A(x)^(1/2).
1, 2, 8, 36, 176, 840, 3312, 4592, -85888, -893664, 1375040, 165097152, 2297399040, -437916544, -676590342400, -13778476089600, -35262701498368, 5528190100333056, 159800245551129600, 1036568296401259520, -77532370748157030400, -3135837171024874272768
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*asinh(x*exp(x))))) -
PARI
a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(k/2+1, k)/((k/2+1)*(n-k)!));
Formula
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380050.
E.g.f.: exp( 2*arcsinh(x*exp(x)) ).
E.g.f.: ( x*exp(x) + sqrt(1 + x^2*exp(2*x)) )^2.
a(n) = n! * Sum_{k=0..n} 2^k * k^(n-k) * binomial(k/2+1,k)/( (k/2+1)*(n-k)! ).