A264889 Partial sums of hyperfactorials (A002109).

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

Offset

0,2

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

Formula

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A002109, A007489, A152690.

Sequence in context: A057771 A056164 A156500 * A365669 A374816 A231537

Adjacent sequences: A264886 A264887 A264888 * A264890 A264891 A264892

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 27 2015

Status

approved