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 A357948 Expansion of e.g.f. exp( x * exp(-x^2) ). 1

%I #29 Oct 29 2022 09:37:59

%S 1,1,1,-5,-23,1,601,2731,-13775,-219743,-313199,15383611,125451481,

%T -811558175,-20767068503,-37852036949,2898343066081,28990920216001,

%U -313289894357855,-8634009894555653,-3214642669500599,2108734127922999361,20183394611962437241

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

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

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

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

%Y Cf. A003725, A358063.

%Y Cf. A216688.

%K sign,easy

%O 0,4

%A _Seiichi Manyama_, Oct 29 2022

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Last modified May 21 15:20 EDT 2024. Contains 372738 sequences. (Running on oeis4.)