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Expansion of e.g.f. exp(x - 5*x^2/2).
2

%I #14 Apr 16 2023 09:47:48

%S 1,1,-4,-14,46,326,-824,-10604,18236,442396,-378224,-22498024,

%T -1695704,1348185736,1458406496,-92914595024,-202295082224,

%U 7230872519696,24425954508736,-626352572263904,-2946818250593824,59688438975796576,369104355288148096

%N Expansion of e.g.f. exp(x - 5*x^2/2).

%H Seiichi Manyama, <a href="/A362279/b362279.txt">Table of n, a(n) for n = 0..649</a>

%F a(n) = a(n-1) - 5*(n-1)*a(n-2) for n > 1.

%F a(n) = n! * Sum_{k=0..floor(n/2)} (-5/2)^k / (k! * (n-2*k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-5*x^2/2)))

%Y Column k=5 of A362277.

%Y Cf. A115331.

%K sign,easy

%O 0,3

%A _Seiichi Manyama_, Apr 13 2023