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A322539
Number of arrays of n integers in -9..9 with sum zero.
2
1, 1, 19, 271, 4579, 78151, 1363573, 24072133, 429042211, 7702189345, 139071924069, 2522948398895, 45949039890469, 839611990929219, 15385356833972711, 282616668487409521, 5202536118941844771, 95950964483217949751, 1772592132899627652691, 32795665902734099555845
OFFSET
0,3
LINKS
FORMULA
a(n) = [x^(9*n)] (Sum_{k=0..18} x^k)^n.
a(n) ~ 19^n / (2*sqrt(15*Pi*n)). - Vaclav Kotesovec, Dec 15 2018
MAPLE
seq(add((-1)^k*binomial(n, k)*binomial(10*n-19*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, 18}]^n], x^(9n)]]; Array[a, 25, 0] (* Amiram Eldar, Dec 14 2018 *)
PROG
(PARI) {a(n) = polcoeff((sum(k=0, 18, x^k))^n, 9*n, x)}
CROSSREFS
Column 9 of A201552.
Sequence in context: A016189 A125476 A016248 * A199819 A016187 A016184
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 14 2018
STATUS
approved