A373720 Expansion of e.g.f. exp(x * (1 + x^2)^3).
1, 1, 1, 19, 73, 541, 5761, 35911, 515089, 5399353, 61253281, 991270171, 11862564121, 203249068309, 3295367161633, 52595413358671, 1060046073787681, 18422593177204081, 383150483373313729, 8042585703164409763, 165930214242407069161, 3968988522451484425741
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, 3*n\7, binomial(3*n-6*k, k)/(n-2*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(3*n/7)} binomial(3*n-6*k,k)/(n-2*k)!.
a(n) == 1 (mod 18).
a(n) = a(n-1) + 9*(n-1)*(n-2)*a(n-3) + 15*(n-1)*(n-2)*(n-3)*(n-4)*a(n-5) + 7*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*a(n-7).