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A318794
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Constant term in the expansion of (Sum_{k=0..2*n} k*(x^k - x^(-k)))^(2*n).
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1
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1, -10, 11628, -166821980, 11017028561336, -2177623431995581080, 1017073493827776256367100, -964251586210215914665050724728, 1668594120314854076064862598821148400, -4872196290698367813554985402532435243198848
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ (-1)^n * c * d^n * n^(4*n - 3/2), where d = 12.176292973966848533089025... and c = 1.04502891160415810516533... - Vaclav Kotesovec, Dec 15 2018
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MATHEMATICA
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a[n_] := If[n==0, 1, Coefficient[Expand[Sum[k * (x^k - x^(-k)), {k, 0, 2n}]^(2n)], x, 0]]; Array[a, 15, 0] (* Amiram Eldar, Dec 15 2018 *)
(* Calculation of constant d: *) 64*(Sin[x]/x^2 - Cos[x]/x)^2 /. FindRoot[(2 - x^2)*Tan[x] == 2*x, {x, 2}, WorkingPrecision -> 70] (* Vaclav Kotesovec, Mar 17 2024 *)
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PROG
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(PARI) {a(n) = polcoeff((sum(k=0, 2*n, k*(x^k-x^(-k))))^(2*n), 0, x)}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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