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A023006
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Number of partitions of n into parts of 7 kinds.
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5
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1, 7, 35, 140, 490, 1547, 4522, 12405, 32305, 80465, 192899, 447146, 1006145, 2204475, 4715510, 9869132, 20247710, 40786690, 80782800, 157510780, 302666903, 573720808, 1073720305, 1985506775, 3630307835, 6567206471, 11760658378, 20860415590, 36665885170, 63891010155, 110415782785, 189320804673, 322174588225
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: Product_{m>=1} 1/(1-x^m)^7.
a(n) ~ 49 * exp(Pi * sqrt(14*n/3)) / (576 * sqrt(2) * n^(5/2)). - Vaclav Kotesovec, Feb 28 2015
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MAPLE
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with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*7, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008
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MATHEMATICA
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nmax=50; CoefficientList[Series[Product[1/(1-x^k)^7, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *)
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PROG
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(PARI) Vec(1/eta('x+O('x^66))^7) /* Joerg Arndt, Jul 30 2011 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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