A102573 Triangle of coefficients of polynomials in Sum_{k=0..n} binomial(n,k)*k^r.

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

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

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