A295519 a(n) = e^3 * Sum_{k=0..n-1} Gamma(k + 1, 3).

0, 1, 5, 22, 100, 493, 2701, 16678, 116704, 923473, 8204077, 81069166, 882762292, 10503611245, 135576241957, 1886597854894, 28151936397856, 448397396131969, 7592570340752053, 136187683731334054, 2579494839314653540, 51445637954467827661

Offset

0,3

Links

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

Formula

a(n) = (3*n-6)*a(n-3)+(4-4*n)*a(n-2)+(3+n)*a(n-1) for n >= 3.

E.g.f.: exp(x+2)*(Ei(1,2-2*x)-Ei(1,2)). - Robert Israel, Dec 17 2017

Maple

a := proc(n) option remember; if n=0 then 0 elif n=1 then 1 elif n=2 then 5 else
(3*n-6)*a(n-3)+(4-4*n)*a(n-2)+(3+n)*a(n-1) fi end: seq(a(n), n=0..21);

Mathematica

a[n_] := E^3 Sum[Gamma[k + 1, 3], {k, 0, n - 1}]; Table[a[n], {n, 0, 21}]

Prog

(PARI) a=vector(1000); a[1]=1; a[2]=5; a[3]=22; for(n=4, #a, a[n] = (n+3)*a[n-1]+(4-4*n)*a[n-2]+(3*n-6)*a[n-3]); va=concat(0, vector(1000, n, a[n])) \\ Altug Alkan, Dec 17 2017

Crossrefs

Cf A053486, A295518.

Sequence in context: A087439 A033452 A346772 * A179602 A262440 A296044

Adjacent sequences: A295516 A295517 A295518 * A295520 A295521 A295522

Keyword

nonn

Author

Peter Luschny, Dec 17 2017

Status

approved