login
A322540
Number of arrays of n integers in -10..10 with sum zero.
2
1, 1, 21, 331, 6181, 116601, 2248575, 43874139, 864287973, 17148949027, 342237634221, 6862175029689, 138132246844879, 2789732439723061, 56501091296763855, 1147129435985083731, 23339695295337149925, 475767618472211229549, 9714486212587875804351
OFFSET
0,3
LINKS
FORMULA
a(n) = [x^(10*n)] (Sum_{k=0..20} x^k)^n.
a(n) ~ sqrt(3) * 21^n / (2*sqrt(55*Pi*n)). - Vaclav Kotesovec, Dec 15 2018
MAPLE
seq(add((-1)^k*binomial(n, k)*binomial(11*n-21*k-1, n-1), k = 0..floor(n/2)), n = 0..20); # Peter Bala, Oct 19 2024
MATHEMATICA
a[n_] := If[n==0, 1, Coefficient[Expand[Sum[x^k, {k, 0, 20}]^n], x^(10n)]]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)
PROG
(PARI) {a(n) = polcoeff((sum(k=0, 20, x^k))^n, 10*n, x)}
CROSSREFS
Column 10 of A201552.
Sequence in context: A011810 A091947 A016195 * A016191 A297336 A095905
KEYWORD
nonn,changed
AUTHOR
Seiichi Manyama, Dec 14 2018
STATUS
approved