A381459 a(n) = (2*n)! * [x^(2*n)] cosh(x)^n.
1, 1, 8, 183, 8320, 628805, 71172096, 11266376947, 2376282177536, 644092653605769, 218152097885716480, 90283850458537906511, 44828889635978905387008, 26302150870235970074916493, 18001952557737056033350615040, 14215240470695667525160827723915
Offset: 0
Keywords
Programs
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Mathematica
Table[(2*n)! * SeriesCoefficient[Cosh[x]^n, {x, 0, 2*n}], {n, 0, 20}] (* Vaclav Kotesovec, May 11 2025 *) -
PARI
a(n) = sum(k=0, n, (n-2*k)^(2*n)*binomial(n, k))/2^n;
Formula
a(n) = (1/2^n) * Sum_{k=0..n} (n-2*k)^(2*n) * binomial(n,k).
a(n) ~ c * ((1-2*r)^2 / (2 * r^r * (1-r)^(1-r)))^n * n^(2*n), where r = 0.015817782507793257357841601600685290637088885324182071456255... is the root of the equation (1-2*r)*(log(1-r) - log(r)) = 4 and c = 2*(1 - 2*r) / sqrt(1 + 4*r - 4*r^2) = 1.879106100687674868112932937483753439332007654254262530564... - Vaclav Kotesovec, May 11 2025, updated May 12 2025