A348314 - OEIS

%I #9 Oct 21 2021 01:25:47

%S 0,1,10,78,568,4120,30864,244720,2088832,19389312,196514560,

%T 2173194496,26128665600,339890756608,4759410116608,71395178280960,

%U 1142340032364544,19419853564641280,349557673401188352,6641597100292636672,132831947503410872320,2789470920661372502016

%N a(n) = n! * Sum_{k=0..n-1} 4^k / k!.

%F E.g.f.: x * exp(4*x) / (1 - x).

%F a(0) = 0; a(n) = n * (a(n-1) + 4^(n-1)).

%F a(n) ~ exp(4)*n!. - _Stefano Spezia_, Oct 11 2021

%t Table[n! Sum[4^k/k!, {k, 0, n - 1}], {n, 0, 21}]

%t nmax = 21; CoefficientList[Series[x Exp[4 x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!

%o (PARI) a(n) = n!*sum(k=0, n-1, 4^k/k!); \\ _Michel Marcus_, Oct 11 2021

%Y Cf. A007526, A053487, A066534, A348312.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Oct 11 2021