|
|
A328812
|
|
Constant term in the expansion of (Product_{k=1..n} (1 + x_k) + Product_{k=1..n} (1 + 1/x_k))^n.
|
|
5
|
|
|
1, 2, 10, 164, 9826, 2031252, 1622278624, 4579408029576, 51207103076632066, 2052124795850957537060, 330463219813679264204224300, 192454957455454582636391397662856, 454577215426865313388106323928590128736, 3907905904547764847197154889183844343802986600
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = A309010(n,n+1) = Sum_{k=0..n} binomial(n,k)^(n+1).
a(n) ~ c * exp(-1/4) * 2^((2*n+1)*(n+1)/2) / (Pi*n)^((n+1)/2), where c = A218792 = Sum_{k = -infinity..infinity} exp(-2*k^2) = 1.271341522189... and c = Sum_{k = -infinity..infinity} exp(-2*(k+1/2)^2) = 1.23528676585389... if n is odd. - Vaclav Kotesovec, May 06 2021
|
|
MATHEMATICA
|
a[n_] := Sum[Binomial[n, k]^(n + 1), {k, 0, n}]; Array[a, 14, 0] (* Amiram Eldar, May 06 2021 *)
|
|
PROG
|
(PARI) {a(n) = sum(k=0, n, binomial(n, k)^(n+1))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|