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A201551
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Number of arrays of n integers in -7..7 with sum zero.
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3
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1, 1, 15, 169, 2255, 30381, 418503, 5832765, 82073295, 1163205475, 16581420835, 237481736823, 3414582082055, 49258226347903, 712601187601395, 10334165623697259, 150186639579545295, 2186774434431445455
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OFFSET
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0,3
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..400 (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]
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FORMULA
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a(n) ~ sqrt(3) * 15^n / (4*sqrt(7*Pi*n)). - Vaclav Kotesovec, Dec 15 2018
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EXAMPLE
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Some solutions for n=5
.-6....6....2...-1...-4...-5...-2...-2....4...-6....2....7...-5...-5....3....5
.-2....0....7...-3....2....6...-3....7...-4...-2...-7...-3....6....2...-3...-7
..0...-6...-5...-2....6....5....5...-5...-6....5....5....1...-4....4....1...-4
..2...-2...-4....0...-7...-5....6...-7....6....6...-5....1....4....5...-3....7
..6....2....0....6....3...-1...-6....7....0...-3....5...-6...-1...-6....2...-1
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MATHEMATICA
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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 *)
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PROG
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(PARI) {a(n) = polcoeff((sum(k=0, 14, x^k))^n, 7*n, x)} \\ Seiichi Manyama, Dec 14 2018
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CROSSREFS
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Column 7 of A201552.
Sequence in context: A016279 A036734 A201041 * A339770 A240276 A206600
Adjacent sequences: A201548 A201549 A201550 * A201552 A201553 A201554
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Dec 02 2011
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EXTENSIONS
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a(0)=1 prepended by Seiichi Manyama, Dec 14 2018
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STATUS
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approved
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