A295518 a(n) = e^2 * Sum_{k=0..n-1} Gamma(k + 1, 2).

0, 1, 4, 14, 52, 220, 1092, 6388, 43588, 341444, 3022660, 29835844, 324782916, 3864151876, 49875956548, 694041238340, 10356520497988, 164956188717892, 2793150548587332, 50100649026499396, 948943120107352900, 18925792541725471556, 396439630395708060484

Offset: 0

Author

Peter Luschny, Dec 17 2017

Keywords

• nonn

Crossrefs

Cf. A010842.

Programs

Maple

a := proc(n) option remember; if n=0 then 0 elif n=1 then 1 elif n=2 then 4 else
(2*n-4)*a(n-3)+(3-3*n)*a(n-2)+(2+n)*a(n-1) fi end: seq(a(n), n=0..22);

Mathematica

a[n_] := E^2 Sum[Gamma[k + 1, 2], {k,0,n-1}]; Table[a[n], {n,0,22}]

Formula

a(n) = (2*n-4)*a(n-3)+(3-3*n)*a(n-2)+(2+n)*a(n-1) for n >= 3.