A365909 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(5*k+2) / (5*k+2)! ).
1, 0, 1, 0, 6, 0, 90, 1, 2520, 72, 113400, 5940, 7484401, 617760, 681084014, 81081000, 81730916280, 13232419201, 12505020896160, 2639867731518, 2376002176470000, 633568693965570, 548870403972290401, 180329793856173720, 151492831528555510516
Offset: 0
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\5, x^(5*k+2)/(5*k+2)!))))
Formula
a(0) = 1; a(n) = Sum_{k=0..floor((n-2)/5)} binomial(n,5*k+2) * a(n-5*k-2).