A144649 Second bisection of A134772.
0, 14400, 134289792000, 29865588836219136000, 64007711015400701105356800000, 799901135455942846519287494400000000000, 42346525471797343063631567858734790430720000000000, 7611746717262781749937067971966455935937523732684800000000000, 3949387898792061570875758855816554982971495343701121923966566400000000000
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..63
Crossrefs
Cf. A134772.
Programs
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Magma
B:=Binomial; F:=Factorial; A134772:= func< n | F(4*n)/(24)^n *(&+[B(n, j)*B(2*n, j)*(-6)^j/(F(j)*B(2*j, j)*B(4*n, 2*j)) : j in [0..n]]) >; A144649:= func< n | A134772(2*n+1) >; [A144649(n): n in [0..20]]; // G. C. Greubel, Oct 13 2023
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Mathematica
A134772[n_]:= ((4*n)!/(24)^n)*Hypergeometric1F1[-n,1/2-2*n,-3/2]; A144549[n_]:= A134772[2*n+1]; Table[A144549[n], {n,0,20}] (* G. C. Greubel, Oct 13 2023 *)
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SageMath
def A134772(n): return (factorial(4*n)/(24)^n)* simplify(hypergeometric([-n], [1/2-2*n], -3/2)) def A144649(n): return A134772(2*n+1) [A144649(n) for n in range(21)] # G. C. Greubel, Oct 13 2023
Formula
a(n) = A134772(2*n+1). - G. C. Greubel, Oct 13 2023
a(n) ~ sqrt(Pi) * 2^(18*n + 11) * n^(8*n + 9/2) / (3^(2*n+1) * exp(8*n + 3/4)). - Vaclav Kotesovec, Oct 21 2023