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A318794
Constant term in the expansion of (Sum_{k=0..2*n} k*(x^k - x^(-k)))^(2*n).
1
1, -10, 11628, -166821980, 11017028561336, -2177623431995581080, 1017073493827776256367100, -964251586210215914665050724728, 1668594120314854076064862598821148400, -4872196290698367813554985402532435243198848
OFFSET
0,2
FORMULA
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
MATHEMATICA
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 *)
PROG
(PARI) {a(n) = polcoeff((sum(k=0, 2*n, k*(x^k-x^(-k))))^(2*n), 0, x)}
CROSSREFS
Cf. A318793.
Sequence in context: A091253 A267887 A151582 * A229229 A190946 A052498
KEYWORD
sign
AUTHOR
Seiichi Manyama, Dec 15 2018
STATUS
approved