A377956 - OEIS

%I #6 Nov 12 2024 09:01:56

%S 1,5,23,103,473,2261,11215,57863,309713,1715653,9831911,58058375,

%T 353546473,2210900693,14215319903,93610866151,632159025185,

%U 4362925851653,30809311250743,221958273142823,1632956199823481,12238229941781845,93509510960341103,726913018468699463

%N a(n) = n! * Sum_{k=0..n} binomial(k+4,n-k) / k!.

%F E.g.f.: (1 + x)^4 * exp(x + x^2).

%F a(n) = -(n-6)*a(n-1) + 3*(n-1)*a(n-2) + 2*(n-1)*(n-2)*a(n-3) for n > 2.

%o (PARI) a(n) = n!*sum(k=0, n, binomial(k+4, n-k)/k!);

%Y Cf. A018191, A047974, A377954, A377955.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Nov 12 2024