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A023004
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Number of partitions of n into parts of 5 kinds.
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5
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1, 5, 20, 65, 190, 506, 1265, 2990, 6765, 14725, 31027, 63505, 126730, 247170, 472295, 885723, 1633000, 2963840, 5302075, 9358470, 16313440, 28107365, 47902010, 80803485, 134992865, 223474667, 366772720, 597049255, 964375855, 1546208695, 2461649861, 3892774130
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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)^5.
a(n) ~ 5^(3/2) * exp(Pi * sqrt(10*n/3)) / (32 * 3^(3/2) * n^2) * (1 - (3*sqrt(6/5) /Pi + 5*sqrt(5/6)*Pi/24) / sqrt(n)). - Vaclav Kotesovec, Feb 28 2015, extended Jan 16 2017
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MAPLE
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with(numtheory): a:=proc(n) option remember; `if`(n=0, 1, add(add(d*5, 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)^5, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *)
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PROG
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(PARI) \ps100 for(n=0, 100, print1((polcoeff(1/eta(x)^5, n, x)), ", "))
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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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