A059356 A diagonal of triangle in A008298.

1, 9, 59, 450, 3394, 30912, 293292, 3032208, 36290736, 433762560, 5925016800, 83648747520, 1335385128960, 20323375994880, 376785057196800, 6493118120294400, 132672192555571200, 2513351450024755200, 56577426980420505600, 1188283280226545664000, 29682641812682686464000, 658094690655791972352000

Offset: 2

Author

N. J. A. Sloane, Jan 27 2001

Keywords

• nonn

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 159.

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..448

Crossrefs

Cf. A000203, A000385, A008298.

Programs

Mathematica

nmax = 30; Table[n!/2 * Sum[DivisorSigma[1, k] * DivisorSigma[1, n-k] / k / (n-k), {k, 1, n-1}], {n, 2, nmax}] (* Vaclav Kotesovec, Nov 09 2020 *)

PARI

{a(n) = my(t='t); n!*polcoef(polcoef(prod(k=1, n, (1-x^k+x*O(x^n))^(-t)), n), 2)} \\ Seiichi Manyama, Nov 07 2020

PARI

{a(n)= (n-1)!*sum(k=1, n-1, sigma(k)*sigma(n-k)/k)} \\ Seiichi Manyama, Nov 09 2020

PARI

{a(n)= n!*sum(k=1, n-1, sigma(k)*sigma(n-k)/(k*(n-k)))/2} \\ Seiichi Manyama, Nov 09 2020

Formula

a(n) = (n-1)! * Sum_{k=1..n-1} sigma(k)*sigma(n-k)/k = (n!/2) * Sum_{k=1..n-1} sigma(k)*sigma(n-k)/(k*(n-k)). - Seiichi Manyama, Nov 09 2020.

E.g.f.: (1/2) * log( Product_{k>=1} (1 - x^k) )^2. - Ilya Gutkovskiy, Apr 24 2021

Extensions

More terms from Vladeta Jovovic, Dec 28 2001