A373758 Expansion of e.g.f. exp(x^4/(24 * (1 - x)^2)).
1, 0, 0, 0, 1, 10, 90, 840, 8435, 91980, 1089900, 13998600, 194184375, 2897744850, 46335539250, 790936146000, 14361717995625, 276491756541000, 5626652076045000, 120696581303298000, 2722068344529158625, 64392333741216731250, 1594243471325576321250
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\4, binomial(n-2*k-1, n-4*k)/(24^k*k!));
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/24*sum(j=4, i, j*(j-3)*v[i-j+1]/(i-j)!)); v;
Formula
a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n-2*k-1,n-4*k)/(24^k * k!).
a(0) = 1; a(n) = ((n-1)!/24) * Sum_{k=4..n} k * (k-3) * a(n-k)/(n-k)!.