login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054651 Triangle T(n,k) read by rows giving coefficients in expansion of n! * Sum_{i=0..n} C(x,i) in descending powers of x. 11
1, 1, 1, 1, 1, 2, 1, 0, 5, 6, 1, -2, 11, 14, 24, 1, -5, 25, 5, 94, 120, 1, -9, 55, -75, 304, 444, 720, 1, -14, 112, -350, 1099, 364, 3828, 5040, 1, -20, 210, -1064, 3969, -4340, 15980, 25584, 40320, 1, -27, 366, -2646, 12873, -31563, 79064, 34236, 270576, 362880 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
Apparently A190782 with reversed rows. - Mathew Englander, May 17 2014
LINKS
EXAMPLE
The first few polynomials are:
1, 1+x, 2+x+x^2, 6+5*x+x^3, 24+14*x+11*x^2-2*x^3+x^4, ...
So the triangle begins:
1;
1, 1;
1, 1, 2;
1, 0, 5, 6;
1, -2, 11, 14, 24;
1, -5, 25, 5, 94, 120;
1, -9, 55, -75, 304, 444, 720;
1, -14, 112, -350, 1099, 364, 3828, 5040;
1, -20, 210, -1064, 3969, -4340, 15980, 25584, 40320;
...
MATHEMATICA
c[n_, k_] := Product[n-i, {i, 0, k-1}]/k!; row[n_] := CoefficientList[ n!*Sum[c[x, k], {k, 0, n}], x] // Reverse; Table[ row[n], {n, 0, 9}] // Flatten (* Jean-François Alcover, Oct 04 2012 *)
CROSSREFS
T(2*n,n) gives A347987.
Sequence in context: A176056 A298213 A130191 * A292323 A059720 A140589
KEYWORD
sign,tabl,nice,easy
AUTHOR
N. J. A. Sloane, Apr 17 2000
EXTENSIONS
Missing 0 corrected by Steve Marak - N. J. A. Sloane, Jul 27 2012
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 12 14:01 EDT 2024. Contains 371635 sequences. (Running on oeis4.)