cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A201551 Number of arrays of n integers in -7..7 with sum zero.

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%I A201551 #25 Oct 19 2024 13:44:24
%S A201551 1,1,15,169,2255,30381,418503,5832765,82073295,1163205475,16581420835,
%T A201551 237481736823,3414582082055,49258226347903,712601187601395,
%U A201551 10334165623697259,150186639579545295,2186774434431445455,31893473567409732813,465851764737061437765
%N A201551 Number of arrays of n integers in -7..7 with sum zero.
%H A201551 Seiichi Manyama, <a href="/A201551/b201551.txt">Table of n, a(n) for n = 0..400</a> (terms 1..210 from R. H. Hardin) [It was suggested that the initial terms of this b-file were wrong, but in fact they are correct. - _N. J. A. Sloane_, Jan 19 2019]
%F A201551 a(n) ~ sqrt(3) * 15^n / (4*sqrt(7*Pi*n)). - _Vaclav Kotesovec_, Dec 15 2018
%e A201551 Some solutions for n=5
%e A201551 .-6....6....2...-1...-4...-5...-2...-2....4...-6....2....7...-5...-5....3....5
%e A201551 .-2....0....7...-3....2....6...-3....7...-4...-2...-7...-3....6....2...-3...-7
%e A201551 ..0...-6...-5...-2....6....5....5...-5...-6....5....5....1...-4....4....1...-4
%e A201551 ..2...-2...-4....0...-7...-5....6...-7....6....6...-5....1....4....5...-3....7
%e A201551 ..6....2....0....6....3...-1...-6....7....0...-3....5...-6...-1...-6....2...-1
%p A201551 seq(add((-1)^k*binomial(n, k)*binomial(8*n-15*k-1, n-1), k = 0..floor(n/2)), n = 0..20); # _Peter Bala_, Oct 19 2024
%t A201551 a[n_] := If[n==0, 1, Coefficient[Expand[Sum[x^k, {k, 0, 14}]^n], x^(7n)]]; Array[a, 25, 0] (* _Amiram Eldar_, Dec 14 2018 *)
%o A201551 (PARI) {a(n) = polcoeff((sum(k=0, 14, x^k))^n, 7*n, x)} \\ _Seiichi Manyama_, Dec 14 2018
%Y A201551 Column 7 of A201552.
%K A201551 nonn
%O A201551 0,3
%A A201551 _R. H. Hardin_, Dec 02 2011
%E A201551 a(0)=1 prepended by _Seiichi Manyama_, Dec 14 2018