login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A146765 Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 1)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]. 0
1, 1, 1, 1, 10, 1, 1, 27, 27, 1, 1, 68, 102, 68, 1, 1, 165, 330, 330, 165, 1, 1, 390, 975, 1300, 975, 390, 1, 1, 903, 2709, 4515, 4515, 2709, 903, 1, 1, 2056, 7196, 14392, 17990, 14392, 7196, 2056, 1, 1, 4617, 18468, 43092, 64638, 64638, 43092, 18468, 4617, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:{1, 2, 12, 56, 240, 992, 4032, 16256, 65280, 261632, 1047552}.

LINKS

Table of n, a(n) for n=0..55.

EXAMPLE

Triangle begins:

{1},

{1, 1},

{1, 10, 1},

{1, 27, 27, 1},

{1, 68, 102, 68, 1},

{1, 165, 330, 330, 165, 1},

{1, 390, 975, 1300, 975, 390, 1},

{1, 903, 2709, 4515, 4515, 2709, 903, 1},

{1, 2056, 7196, 14392, 17990, 14392, 7196, 2056, 1},

{1, 4617, 18468, 43092, 64638, 64638, 43092, 18468, 4617, 1},

{1, 10250, 46125, 123000, 215250, 258300, 215250, 123000, 46125, 10250, 1}

MATHEMATICA

p[x_, n_] = If[ n == 0, 1, (x + 1)^n + 2^(n - 1)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]];

Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]

CROSSREFS

Sequence in context: A113280 A159041 A154979 * A190152 A154984 A173047

Adjacent sequences:  A146762 A146763 A146764 * A146766 A146767 A146768

KEYWORD

nonn,tabl,less

AUTHOR

Roger L. Bagula, Nov 02 2008

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 December 5 20:39 EST 2021. Contains 349558 sequences. (Running on oeis4.)