A373742 Expansion of e.g.f. exp(x^3/6 * (1 + x)).
1, 0, 0, 1, 4, 0, 10, 140, 560, 280, 8400, 92400, 385000, 800800, 16816800, 169569400, 784784000, 3811808000, 68803134400, 673546473600, 3693641952000, 30454440016000, 507477434464000, 5002277568288000, 33870732912016000, 386622918281600000
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\3, binomial(k, n-3*k)/(6^k*k!));
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} binomial(k,n-3*k)/(6^k * k!).
a(n) = (n-1)*(n-2)/6 * (3*a(n-3) + 4*(n-3)*a(n-4)).