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A298851
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a(n) = [x^n] Product_{k=1..n} 1/(1-k^2*x).
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8
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1, 1, 21, 1408, 196053, 46587905, 16875270660, 8657594647800, 5974284925007685, 5336898188553325075, 5992171630749371157181, 8260051854943114812198756, 13714895317396748230146099660, 26998129079190909699998105620908, 62173633286588800021263427046090792
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ c * d^n * n^(2*n - 1/2), where d = 1.774513671664430848697327843228386312953174421074432567764556466987... and c = 0.617929515483613293691991371141292259390065108300160936187723552669... - Vaclav Kotesovec, Feb 02 2018
a(n) = 2*(Sum_{k=0..n} (n-k)^(4*n)/((2*n-k)!*k!*(-1)^k)) for n>0 - Tani Akinari, Mar 09 2021
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MAPLE
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b:= proc(k, n) option remember; `if`(k=0, 1,
add(b(k-1, j)*j^2, j=1..n))
end:
a:= n-> b(n$2):
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MATHEMATICA
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Table[SeriesCoefficient[Product[1/(1 - k^2*x), {k, 1, n}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 02 2018 *)
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PROG
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(Maxima) a(n):=if n<1 then 1 else 2*sum((n-k)^(4*n)/((2*n-k)!*k!*(-1)^k), k, 0, n);
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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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