A264889 Partial sums of hyperfactorials (A002109).

1, 2, 6, 114, 27762, 86427762, 4031164827762, 3319770429936027762, 55696441261496986915227762, 21577941278638297470665013744027762, 215779412250996503370318565758665013744027762, 61564384586850833363801728392684283449726665013744027762

Offset: 0

Author

Ilya Gutkovskiy, Nov 27 2015

Keywords

• nonn

Examples

			a(0) = 1;
a(1) = 1 + 1^1 = 2;
a(2) = 1 + 1^1 + 1^1*2^2 = 6;
a(3) = 1 + 1^1 + 1^1*2^2 + 1^1*2^2*3^3 = 114;
a(4) = 1 + 1^1 + 1^1*2^2 + 1^1*2^2*3^3 + 1^1*2^2*3^3*4^4 = 27762, etc.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..37
• Eric Weisstein's World of Mathematics, Hyperfactorial
• Eric Weisstein's World of Mathematics, Barnes G-Function

Crossrefs

Cf. A002109, A007489, A152690.

Programs

Mathematica

Table[Sum[Hyperfactorial[k], {k, 0, n}], {n, 0, 11}]
Accumulate[Hyperfactorial[Range[0,15]]] (* Harvey P. Dale, Sep 22 2021 *)

PARI

a(n) = sum(k=0, n, prod(j=2, k, j^j)); \\ Altug Alkan, Nov 27 2015

Formula

a(n) = Sum_{k = 0..n} A002109(k).

a(n) = Sum_{k = 0..n} (k!)^k/Barnes G-Function(k + 1).