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Search: id:A137373
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| A137373 |
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Triangular sequence from coefficients of Gould polynomials for the special case :n=a=b; g(x,n)=(x/(x - n^2))*Binomial[x - n^2, n]. |
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+0
1
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| 1, 0, 1, 0, -5, 1, 0, 110, -21, 1, 0, -5814, 971, -54, 1, 0, 570024, -83050, 4535, -110, 1, 0, -89927760, 11544394, -592605, 15205, -195, 1, 0, 20872566000, -2387965020, 113809024, -2892225, 41335, -315, 1, 0, -6702649153200, 690576361740, -30488594444, 747700849, -11000360, 97090, -476, 1, 0
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are: {1, 1, -4, 90, -4896, 491400, -78960960, 18595558800, -6041824588800, 2591645234048640, -1419367337623872000}
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REFERENCES
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Weisstein, Eric W. "Gould Polynomial." http://mathworld.wolfram.com/GouldPolynomial.html
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FORMULA
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g(x,n)=G[x,n,a,b];a=b=n; g(x,n)=(x/(x - n^2))*Binomial[x - n^2, n] out{n,m)=n!*Coefficients(g(x,n))
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EXAMPLE
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{1},
{0, 1},
{0, -5, 1},
{0, 110, -21, 1},
{0, -5814, 971, -54, 1},
{0, 570024, -83050, 4535, -110, 1},
{0, -89927760,11544394, -592605, 15205, -195, 1},
{0,20872566000, -2387965020, 113809024, -2892225, 41335, -315, 1},
{0, -6702649153200, 690576361740, -30488594444, 747700849, -11000360, 97090, -476, 1},
{0, 2847610195436160, -266634653035536, 10921595032844, -255607078356, 3738480249, -34990704, 204666, -684, 1},
{0, -1547110398010020480, 132689735745966576, -5057524107776700, 112440435753680, -1606899405825, 15308433273, -97218450, 396870, -945, 1}
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MATHEMATICA
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Clear[a, g] g[x_, n_] := (x/(x - n^2))*Binomial[x - n^2, n]; Table[ExpandAll[n!*g[x, n]], {n, 0, 10}]; a = Table[CoefficientList[n!*g[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Adjacent sequences: A137370 A137371 A137372 this_sequence A137374 A137375 A137376
Sequence in context: A019183 A019156 A112991 this_sequence A086464 A146306 A119788
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 09 2008
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