A350595 a(n) = Sum_{k=0..2*n} (-1)^(n+k) * binomial(2*n,k)^n.
1, 0, 6, 1680, 5562130, 248832363780, 157933807781230404, 1459371378373349655614400, 199540356506880704345957381087490, 408278793226256174470138460253382778465100, 12605249484391847030759523774663513363531264829120276
Offset: 0
Keywords
Programs
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Mathematica
Table[Sum[(-1)^(n+k)*Binomial[2*n,k]^n,{k,0,2n}],{n,0,10}] (* Stefano Spezia, Jan 08 2022 *) -
PARI
a(n) = sum(k=0, 2*n, (-1)^(n+k)*binomial(2*n, k)^n);
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Python
from math import comb def A350595(n): return sum((-1 if (n+k) % 2 else 1)*comb(2*n,k)**n for k in range(2*n+1)) # Chai Wah Wu, Jan 08 2022
Formula
a(n) ~ c * A224733 = c * binomial(2*n, n)^n, where c = 0.30062580086898437298921168710510240913792796183034926496082316066508397... - Vaclav Kotesovec, Jan 15 2022