OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..56
FORMULA
a(n) ~ c * exp(-1/4) * 2^(n^2 - n/2) * n^(n/2) / Pi^(n/2), where c = Sum_{k = -infinity..infinity} exp(-2*k*(k-1)) = exp(1/2) * sqrt(Pi/2) * EllipticTheta(3, -Pi/2, exp(-Pi^2/2)) = 2.036643566277677716389243890291939003151565... if n is even and c = Sum_{k = -infinity..infinity} exp(-2*k^2 + 1/2) = exp(1/2) * EllipticTheta(3, 0, exp(-2)) = 2.096087809957308346119920713317351288828811... if n is odd.
a(n) = n^n * A328812(n-1) for n > 0. - Seiichi Manyama, Jul 15 2020
MATHEMATICA
Flatten[{1, Table[Sum[k^n*Binomial[n, k]^n, {k, 1, n}], {n, 1, 15}]}]
PROG
(PARI) a(n) = if (n==0, 1, sum(k=0, n, k^n * binomial(n, k)^n)); \\ Michel Marcus, Jul 13 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 12 2020
STATUS
approved