A348314 a(n) = n! * Sum_{k=0..n-1} 4^k / k!.

0, 1, 10, 78, 568, 4120, 30864, 244720, 2088832, 19389312, 196514560, 2173194496, 26128665600, 339890756608, 4759410116608, 71395178280960, 1142340032364544, 19419853564641280, 349557673401188352, 6641597100292636672, 132831947503410872320, 2789470920661372502016

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

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

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

a(n) ~ exp(4)*n!. - Stefano Spezia, Oct 11 2021

Mathematica

Table[n! Sum[4^k/k!, {k, 0, n - 1}], {n, 0, 21}]
nmax = 21; CoefficientList[Series[x Exp[4 x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) a(n) = n!*sum(k=0, n-1, 4^k/k!); \\ Michel Marcus, Oct 11 2021

Crossrefs

Cf. A007526, A053487, A066534, A348312.

Sequence in context: A082136 A153596 A316595 * A056986 A243247 A222701

Adjacent sequences: A348311 A348312 A348313 * A348315 A348316 A348317

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 11 2021

Status

approved