A375655 Expansion of e.g.f. exp(x^2 + x * exp(x^2/2)).
1, 1, 3, 10, 37, 186, 931, 5608, 36345, 252892, 1961011, 15811896, 139137373, 1286591320, 12584565267, 130564271776, 1410581283121, 16095825151248, 190917669584035, 2366869021623712, 30550349329738581, 408806590130340256, 5688859328729212483
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2+x*exp(x^2/2)))) -
PARI
a(n) = n!*sum(k=0, n\2, ((n-2*k+2)/2)^k/(k!*(n-2*k)!));
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} ((n-2*k+2)/2)^k / (k! * (n-2*k)!).