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A059356 A diagonal of triangle in A008298. 4
1, 9, 59, 450, 3394, 30912, 293292, 3032208, 36290736, 433762560, 5925016800, 83648747520, 1335385128960, 20323375994880, 376785057196800, 6493118120294400, 132672192555571200, 2513351450024755200, 56577426980420505600, 1188283280226545664000, 29682641812682686464000, 658094690655791972352000 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified March 6 01:33 EST 2021. Contains 341835 sequences. (Running on oeis4.)