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A059356
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A diagonal of triangle in A008298.
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4
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1, 9, 59, 450, 3394, 30912, 293292, 3032208, 36290736, 433762560, 5925016800, 83648747520, 1335385128960, 20323375994880, 376785057196800, 6493118120294400, 132672192555571200, 2513351450024755200, 56577426980420505600, 1188283280226545664000, 29682641812682686464000, 658094690655791972352000
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OFFSET
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2,2
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 159.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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