login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 20 06:50 EST 2019. Contains 319325 sequences. (Running on oeis4.)