A383853 a(n) = Sum_{k=0..n} binomial(2*n, k) * (n-k)^(4*n).

1, 1, 260, 556032, 4641176128, 106519579045760, 5472276566891956224, 549375993583284180705280, 97867116732573493470161420288, 28783909470167571938915053763592192, 13216052972619446942074113385580542689280, 9058922175695195359062480694771506779050213376

Offset

0,3

Links

Table of n, a(n) for n=0..11.

Formula

a(n) = Sum_{k=0..n} binomial(2*n, n+k) * k^(4*n).

a(n) ~ 4^n * r^(4*n+1) * n^(4*n) / (sqrt(2 - r^2) * (1 - r^2)^n * exp(4*n)), where r = 0.9683644349844134852843167967986294187258222293516... is the root of the equation (1+r)/(1-r) = exp(4/r).

Mathematica

Join[{1}, Table[Sum[Binomial[2*n, k]*(n-k)^(4*n), {k, 0, n}], {n, 1, 12}]] (* or *)
Join[{1}, Table[Sum[Binomial[2*n, n+k]*k^(4*n), {k, 0, n}], {n, 1, 12}]]

Crossrefs

Cf. A209289, A298851, A345876.

Sequence in context: A216940 A395713 A200578 * A200808 A350084 A280325

Adjacent sequences: A383850 A383851 A383852 * A383854 A383855 A383856

Keyword

nonn

Author

Vaclav Kotesovec, May 12 2025

Status

approved