A377956 a(n) = n! * Sum_{k=0..n} binomial(k+4,n-k) / k!.
1, 5, 23, 103, 473, 2261, 11215, 57863, 309713, 1715653, 9831911, 58058375, 353546473, 2210900693, 14215319903, 93610866151, 632159025185, 4362925851653, 30809311250743, 221958273142823, 1632956199823481, 12238229941781845, 93509510960341103, 726913018468699463
Offset: 0
Programs
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PARI
a(n) = n!*sum(k=0, n, binomial(k+4, n-k)/k!);
Formula
E.g.f.: (1 + x)^4 * exp(x + x^2).
a(n) = -(n-6)*a(n-1) + 3*(n-1)*a(n-2) + 2*(n-1)*(n-2)*a(n-3) for n > 2.