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!)
A142073 A triangular sequence of coefficients of and infinite sum polynomial: p(x,n)=(1 - 2*x)^(n + 1)*Sum[k^n*(x/(1 - x))^k, {k, 0, Infinity}]/x; p(x,n)=(1 - 2*x)^(n + 1)*PolyLog[ -n,x/(1-x)]/x;. 1
1, 1, -1, 1, -1, 1, 1, -4, 2, 1, 7, -16, 8, 1, 21, -28, -26, 48, -16, 1, 51, 32, -356, 408, -136, 1, 113, 492, -1774, 1072, 912, -1088, 272, 1, 239, 2592, -5008, -6656, 20736, -15872, 3968, 1, 493, 10628, -50, -94432, 154528, -57856, -45056, 39680, -7936, 1, 1003, 38768, 108820, -621352, 455608, 848384 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,8
COMMENTS
Except for n=0, the row sums are zero.
LINKS
FORMULA
p(x,n)=(1 - 2*x)^(n + 1)*Sum[k^n*(x/(1 - x))^k, {k, 0, Infinity}]/x; p(x,n)=(1 - 2*x)^(n + 1)*PolyLog[ -n,x/(1-x)]/x; t(n,m)=coefficients(p(x,n)).
p(x,n)=Sum(eulerian(n,k)*(x-1)^(k+1),k=0..n); t(n,m)=Coefficients(p(x,n)). [From Mourad Rahmani (mrahmani(AT)usthb.dz), Aug 29 2010]
EXAMPLE
{1},
{1, -1},
{1, -1},
{1, 1, -4, 2},
{1, 7, -16, 8},
{1, 21, -28, -26, 48, -16},
{1, 51, 32, -356, 408, -136},
{1, 113, 492, -1774, 1072, 912, -1088,272},
{1, 239, 2592, -5008, -6656, 20736, -15872, 3968},
{1, 493, 10628, -50, -94432, 154528, -57856, -45056, 39680, -7936},
{1, 1003, 38768, 108820, -621352, 455608, 848384, -1538816, 884480, -176896}
MATHEMATICA
p[x_, n_] = (1 - 2*x)^(n + 1)*Sum[k^n*(x/(1 - x))^k, {k, 0, Infinity}]/x; Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]
CROSSREFS
Cf. A141720.
Cf. A008292 [From Mourad Rahmani (mrahmani(AT)usthb.dz), Aug 29 2010]
Sequence in context: A136249 A142147 A291977 * A193559 A135294 A175938
KEYWORD
sign,uned
AUTHOR
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 March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)