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A060944 a(n) = n!^2 * Sum_{k=1..n} Sum_{j=1..k} 1/j^2. 1
1, 9, 130, 2900, 93576, 4141872, 241353792, 17929776384, 1655071418880, 185914776960000, 24978180045312000, 3955930130221056000, 729464836964806656000, 154952762244805582848000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sum of generalized harmonic numbers squared multiplied by (n!)^2. a(n) = Sum_{k=1..n} HarmonicNumber(k, 2), where HarmonicNumber(k, 2) = Sum_{k = 1..n} 1/k^2. - Alexander Adamchuk, Oct 27 2004

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Harmonic Number.

FORMULA

a(n) = (n!)^2 * Sum[(k+1)/(n-k)^2, {k, 0, n-1}], a(n) = (n!)^2 * Sum[HarmonicNumber[k, 2]], {k, 1, n}], HarmonicNumber[k, 2] = A007406(k) / A007407(k). - Alexander Adamchuk, Oct 27 2004

EXAMPLE

a(3) = 6^2 *(1 + (1 + 1/2^2) + (1 + 1/2^2 + 1/3^2)) = 130.

MATHEMATICA

Table[(n!)^2*Sum[(k+1)/(n-k)^2, {k, 0, n-1}], {n, 1, 10}]

PROG

(PARI) a(n)={n!^2 * sum(k=1, n, sum(j=1, k, 1/j^2))} \\ Harry J. Smith, Jul 15 2009

CROSSREFS

Cf. A001705, A007406, A007407.

Sequence in context: A184143 A287690 A075762 * A299596 A200407 A194895

Adjacent sequences:  A060941 A060942 A060943 * A060945 A060946 A060947

KEYWORD

easy,nonn

AUTHOR

Leroy Quet, May 07 2001

STATUS

approved

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Last modified May 25 01:17 EDT 2019. Contains 323534 sequences. (Running on oeis4.)