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A336204
a(n) = Sum_{k=0..n} 2^k * binomial(n,k)^n.
6
1, 3, 13, 171, 7761, 1256283, 741398869, 1609036666443, 13118066779885825, 399221556627301207443, 46476897754761801245056293, 20377119057713827002258336842283, 34592895120825704155462768381947657489, 222457046333769635263635086646525921070978443
OFFSET
0,2
LINKS
FORMULA
a(n) ~ c * 2^(n*(n+1)) / (Pi*n)^(n/2), where c = exp(-1/4) * Sum_{k = -oo..oo} 2^k * exp(-2*k^2) = 1.0434092897163574491113380912895917... if n is even and c = exp(-1/4) * Sum_{k = -oo..oo} 2^(k + 1/2) * exp(-2*(k + 1/2)^2) = 1.029587234777114329090639723058125257... if n is odd. - Vaclav Kotesovec, Jul 12 2020
MATHEMATICA
Table[Sum[2^k*Binomial[n, k]^n, {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 12 2020 *)
PROG
(PARI) {a(n) = sum(k=0, n, 2^k*binomial(n, k)^n)};
(Magma) [(&+[2^j*Binomial(n, j)^n: j in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 31 2022
(SageMath)
def A336204(n): return sum(2^k*binomial(n, k)^n for k in (0..n))
[A336204(n) for n in (0..20)] # G. C. Greubel, Aug 31 2022
CROSSREFS
Main diagonal of A336203.
Sequence in context: A290769 A213794 A239979 * A261361 A114317 A168320
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 11 2020
STATUS
approved