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 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}] 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 A231537 A303441 Adjacent sequences: A264886 A264887 A264888 * A264890 A264891 A264892 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Nov 27 2015 STATUS approved

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Last modified April 21 14:48 EDT 2024. Contains 371874 sequences. (Running on oeis4.)