login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A264889 Partial sums of hyperfactorials (A002109). 1
1, 2, 6, 114, 27762, 86427762, 4031164827762, 3319770429936027762, 55696441261496986915227762, 21577941278638297470665013744027762, 215779412250996503370318565758665013744027762, 61564384586850833363801728392684283449726665013744027762 (list; graph; refs; listen; history; text; internal format)
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}]

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 * A231537 A303441 A075391

Adjacent sequences:  A264886 A264887 A264888 * A264890 A264891 A264892

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 27 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 19 10:36 EDT 2019. Contains 323390 sequences. (Running on oeis4.)