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 A102573 Triangle of coefficients of polynomials in Sum_{k=0..n} binomial(n,k)*k^r. 6
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS For a table of coefficients of these polynomials without factors removed see A209849. - Peter Bala, Mar 16 2012 REFERENCES 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 LINKS Eric Weisstein's World of Mathematics, Binomial Sums EXAMPLE 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) CROSSREFS Sequence in context: A101350 A199478 A134867 * A233940 A134033 A185051 Adjacent sequences:  A102570 A102571 A102572 * A102574 A102575 A102576 KEYWORD sign,tabl AUTHOR Eric W. Weisstein, Jan 15 2005 STATUS approved

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Last modified October 20 15:22 EDT 2018. Contains 316388 sequences. (Running on oeis4.)