A375651 Expansion of e.g.f. exp(x + x^2 * exp(x)).
1, 1, 3, 13, 61, 341, 2221, 16045, 127065, 1097353, 10231561, 102133241, 1085537509, 12228389629, 145369356861, 1816987580101, 23804010114481, 325966118893457, 4654236956576977, 69138950655122929, 1066449047096819901, 17050138691821539781
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x+x^2*exp(x)))) -
PARI
a(n) = n!*sum(k=0, n\2, (k+1)^(n-2*k)/(k!*(n-2*k)!));
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(n-2*k) / (k! * (n-2*k)!).