A394716 - OEIS

A394716

a(n) = Sum_{1 <= i < j <= n} ( n!/(i*j) )^3.

0, 0, 1, 36, 2555, 335655, 74550304, 26015028256, 13472453691584, 9899759488178880, 9956935441072958976, 13309904809688027245056, 23075728090638862938144768, 50829133553976135556548919296, 139764726764087926884028696756224, 472500813583621452881213310763008000

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OFFSET

0,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..181

Eric Weisstein's World of Mathematics, Harmonic Number

FORMULA

a(n) = (n!)^3 * (H(n,3)^2 - H(n,6))/2 where H(n,r) = Sum_{k=1..n} 1/k^r.

a(n) = A249677(n,n-2) = [x^(n-2)] Product_{k=0..n} (1 + k^3*x).

a(n) = (n^3 + (n-1)^3) * a(n-1) - (n-1)^6 * a(n-2) + ((n-2)!)^3 for n > 1.

PROG

(PARI) a(n) = polcoef(prod(k=0, n, 1+k^3*x), n-2);