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A102573
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Triangle of coefficients of polynomials in Sum_{k=0..n} binomial(n,k)*k^r.
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6
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1, 1, 3, 1, 5, -2, 1, 10, 15, -10, 1, 14, 31, -46, 16, 1, 21, 105, 35, -210, 112, 1, 27, 183, 97, -832, 860, -272, 1, 36, 378, 1008, -1575, -2436, 5292, -2448, 1, 44, 586, 2144, -3719, -10876, 31036, -26896, 7936, 1, 55, 990, 6270, 3465, -51513, 27720, 135300, -208560
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OFFSET
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2,3
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COMMENTS
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For a table of coefficients of these polynomials without factors removed see A209849. - Peter Bala, Mar 16 2012
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REFERENCES
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E. Kilic, Y. T. Ulutas and N. Omur, Formulas for weighted binomial sums using the powers of terms of binary recurrences, Miskolc Mathematical Notes, Vol. 13 (2012), No. 1, pp. 53-65. - From N. J. A. Sloane, Dec 16 2012
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LINKS
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EXAMPLE
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1;
1, 3;
1, 5, -2;
1, 10, 15, -10;
1, 14, 31, -46, 16;
...
E.g. Sum[binomial[n,k]k^4,{k,0,n}] = 2^(-4 + n)*n*(1 + n)*(-2 + 5*n + n^2)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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