A373707 Expansion of e.g.f. exp(x * (1 + x^3)^2).
1, 1, 1, 1, 49, 241, 721, 6721, 124321, 913249, 4243681, 94818241, 1640604241, 14642181841, 131026944049, 3669304504321, 62536989802561, 627395160826561, 10818406189690561, 308036857749752449, 5219006583104930161, 65146235714284117681
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, 2*n\7, binomial(2*n-6*k, k)/(n-3*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(2*n/7)} binomial(2*n-6*k,k)/(n-3*k)!.
a(n) == 1 (mod 48).
a(n) = a(n-1) + 8*(n-1)*(n-2)*(n-3)*a(n-4) + 7*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*a(n-7).