A375410 - OEIS

%I #11 Aug 14 2024 09:16:51

%S 1,0,5,-4,81,-176,2605,-8100,137249,-424576,10376181,-21429860,

%T 1069514545,279470736,149969551901,616166705084,28838719110465,

%U 261581059999360,7560615053166949,106911086586605244,2626348956282622481,48474495094075756880,1160413567193463596685

%N Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x).

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

%F D-finite with recurrence a(n) +(-n+1)*a(n-1) +5*(-n+1)*a(n-2) +7*(n-1)*(n-2)*a(n-3) -3*(n-1)*(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Aug 14 2024

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^2)/(1-x)))

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

%Y Cf. A375409, A375411.

%Y Cf. A375413, A375415.

%K sign

%O 0,3

%A _Seiichi Manyama_, Aug 14 2024