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Expansion of e.g.f. exp(x + x^2 * exp(x)).
1

%I #9 Aug 23 2024 02:11:42

%S 1,1,3,13,61,341,2221,16045,127065,1097353,10231561,102133241,

%T 1085537509,12228389629,145369356861,1816987580101,23804010114481,

%U 325966118893457,4654236956576977,69138950655122929,1066449047096819901,17050138691821539781

%N Expansion of e.g.f. exp(x + x^2 * exp(x)).

%F a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(n-2*k) / (k! * (n-2*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x+x^2*exp(x))))

%o (PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(n-2*k)/(k!*(n-2*k)!));

%Y Cf. A216507, A375652.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 22 2024