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A099827 Generalized harmonic number H(n,5) multiplied by (n!)^5. H(n,5) = Sum_{k=1..n} 1/k^5. H(n,5) = 1, 33/32, 8051/7776, 257875/248832,... (A099828 - numerator). 11
0, 1, 33, 8051, 8252000, 25795462624, 200610400564224, 3371852494046112768, 110492114540967125581824, 6524555433591956305924325376, 652461835742417609568446054400000, 105080260346474296336209157187174400000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Note a(n) is divisible by n, except when n is prime or n=0. a(n+1) is divisible by n, except when n is prime or n=0.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..120

Eric Weisstein's World of Mathematics, Harmonic Number

FORMULA

a(n) = (n!)^5 * Sum[1/k^5, {k, 1, n}] a(n) = (n!)^5 * HarmonicNumber[n, 5]

a(0) = 0, a(1) = 1, a(n+1) = (n^5+(n+1)^5)*a(n) - n^10*a(n-1) for n > 0. - Seiichi Manyama, Aug 24 2017

a(n) ~ Zeta(5) * (2*Pi)^(5/2) * n^(5*n+5/2) / exp(5*n). - Vaclav Kotesovec, Aug 27 2017

EXAMPLE

a(2) = (2!)^5 * (1 + 1/2^5) = 2^5 + 1 = 33,

a(3) = (3!)^5 * (1 + 1/2^5 + 1/3^5) = 6^5 + 3^5 + 1 = 8051.

MATHEMATICA

Table[(n!)^5*Sum[1/k^5, {k, 1, n}], {n, 0, 13}] or Table[(n!)^5*HarmonicNumber[n, 5], {n, 0, 13}]

CROSSREFS

Cf. A001819, A008515, A099828, A001008.

Column k=5 of A291556.

Sequence in context: A219563 A183237 A099828 * A269793 A060705 A061687

Adjacent sequences:  A099824 A099825 A099826 * A099828 A099829 A099830

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Oct 27 2004

EXTENSIONS

a(0)=0 prepended by Seiichi Manyama, Aug 23 2017

STATUS

approved

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)