A365973 - OEIS

%I #9 Sep 24 2023 09:16:09

%S 1,0,0,2,0,0,40,720,0,2240,172800,3628800,246400,49420800,3531340800,

%T 87223136000,18450432000,3006222336000,225434879488000,

%U 6411312940032000,2744461025280000,435228787435520000,35074217524469760000,1126838040745697280000

%N Expansion of e.g.f. exp( Sum_{k>=0} x^(4*k+3) / (4*k+3) ).

%F a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-3)/4)} a(n-4*k-3)/(n-4*k-3)!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\4, x^(4*k+3)/(4*k+3)))))

%Y Cf. A038205, A130915, A365974.

%Y Cf. A365981.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Sep 23 2023