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A348082
a(n) = [x^n] Product_{k=1..2*n} 1/(1 - (2*k-1)^2 * x).
2
1, 10, 5082, 8187608, 27350858986, 155829826875450, 1352947132455198360, 16634466165612256277904, 275064994463136775255491210, 5887721317348514340055453080350, 158391364687146632772523433272637642, 5231238431447353406197858182627897590880
OFFSET
0,2
FORMULA
a(n) ~ c * d^n * n!^2 / n^(3/2), where d = 314.10823271731893046905221731661671603309238326838259911942334135410817... and c = 0.041829340046147280338756273441751288807538817430199591424694081075... - Vaclav Kotesovec, Oct 16 2021
MATHEMATICA
Table[SeriesCoefficient[Product[1/(1 - (2*k-1)^2*x), {k, 1, 2*n}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 16 2021 *)
PROG
(PARI) a(n) = polcoef(1/prod(k=1, 2*n, 1-(2*k-1)^2*x+x*O(x^n)), n);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 27 2021
STATUS
approved