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

2,2

References

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

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A000203, A000385, A008298.

Sequence in context: A026717 A231228 A198847 * A039929 A099333 A098327

Adjacent sequences: A059353 A059354 A059355 * A059357 A059358 A059359

Keyword

nonn

Author

N. J. A. Sloane, Jan 27 2001

Extensions

More terms from Vladeta Jovovic, Dec 28 2001

Status

approved