

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
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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. 5365.  From N. J. A. Sloane, Dec 16 2012


LINKS

Table of n, a(n) for n=2..55.
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

A209849.
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



