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A083669
Number of ordered quintuples (a,b,c,d,e), -n <= a,b,c,d,e <= n, such that a+b+c+d+e = 0.
5
1, 51, 381, 1451, 3951, 8801, 17151, 30381, 50101, 78151, 116601, 167751, 234131, 318501, 423851, 553401, 710601, 899131, 1122901, 1386051, 1692951, 2048201, 2456631, 2923301, 3453501, 4052751, 4726801, 5481631, 6323451, 7258701
OFFSET
0,2
FORMULA
a(n) = 1 + 5*n*(n+1)*(23*n^2 + 23*n + 14)/12.
a(n) = (1/Pi)*Integral_{x=0..Pi} (sin((n+1/2)*x)/sin(x/2))^5. - Yalcin Aktar, Dec 03 2011
G.f.: ( -1 - 46*x - 136*x^2 - 46*x^3 - x^4 ) / (x-1)^5. - R. J. Mathar, Dec 17 2011
a(n) = [x^(5*n)] (Sum_{k=0..2*n} x^k)^5. - Seiichi Manyama, Dec 14 2018
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 51, 381, 1451, 3951}, 30] (* Vincenzo Librandi, Dec 15 2018 *)
PROG
(PARI) a(n)=115/12*n^4+115/6*n^3+185/12*n^2+35/6*n+1
(PARI) {a(n) = polcoeff((sum(k=0, 2*n, x^k))^5, 5*n, x)} \\ Seiichi Manyama, Dec 14 2018
(Magma) [1+5*n*(n+1)*(23*n^2+23*n+14)/12: n in [0..30]]; // Vincenzo Librandi, Dec 15 2018
CROSSREFS
Row 5 of A201552.
Sequence in context: A165087 A359026 A152579 * A273189 A222910 A259692
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Jun 14 2003
STATUS
approved