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%I #9 Aug 23 2024 02:12:14
%S 1,1,3,13,49,321,1891,13693,113793,942049,9428131,93837261,1043918833,
%T 12318170593,151123106499,2024107965181,27672074520961,
%U 406722703307073,6188268876372163,98499148173678349,1645657615850089521,28317883192163927041
%N Expansion of e.g.f. exp(x^2 + x * exp(x^2)).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^k / (k! * (n-2*k)!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2+x*exp(x^2))))
%o (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+1)^k/(k!*(n-2*k)!));
%Y Cf. A216688, A375654.
%Y Cf. A375604.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 22 2024