A365895 Expansion of e.g.f. exp( Sum_{k>=0} x^(5*k+4) / (5*k+4)! ).
1, 0, 0, 0, 1, 0, 0, 0, 35, 1, 0, 0, 5775, 715, 1, 0, 2627625, 850850, 27370, 1, 2546168625, 1697445750, 189019600, 826045, 4509264634876, 5368172184375, 1385034901250, 52398292375, 13189599083995050, 25499891510218126, 12524921737453125
Offset: 0
Keywords
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\5, x^(5*k+4)/(5*k+4)!))))
Formula
a(0)=1; a(n) = Sum_{k=0..floor((n-4)/5)} binomial(n-1,5*k+3) * a(n-5*k-4).