cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A143506 Irregular triangle read by rows: first row is 1, and n-th row gives the coefficients of x^(n - 1)*R(n,x + 1/x)/(x + 1/x), where R(n,x) is the n-th row polynomial for A060187.

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 3, 6, 1, 1, 23, 26, 47, 26, 23, 1, 1, 76, 234, 304, 467, 304, 234, 76, 1, 1, 237, 1687, 2630, 5293, 4787, 5293, 2630, 1687, 237, 1, 1, 722, 10549, 27158, 52730, 78586, 84365, 78586, 52730, 27158, 10549, 722, 1, 1, 2179, 60664, 272797, 563029, 1132234
Offset: 0

Views

Author

Roger L. Bagula and Gary W. Adamson, Oct 25 2008

Keywords

Comments

Row sums yield A080253.

Examples

			Triangle begins:
   1;
   1,   1,    1;
   1,   6,    3,    6,    1;
   1,  23,   26,   47,   26,   23,    1;
   1,  76,  234,  304,  467,  304,  234,   76,    1;
   1, 237, 1687, 2630, 5293, 4787, 5293, 2630, 1687, 237, 1;
    ... reformatted. - _Franck Maminirina Ramaharo_, Oct 25 2018
		

Crossrefs

Programs

  • Mathematica
    Table[CoefficientList[FullSimplify[ExpandAll[2^n*(1 - x - 1/x)^(1 + n)*x^n*LerchPhi[x + 1/x, -n, 1/2]]], x], {n, 0, 10}]//Flatten

Formula

Row n is generated by the polynomial 2^n*(1 - x - 1/x)^(1 + n)*x^n*Phi(x + 1/x, -n, 1/2), where Phi is the Lerch transcendant.
E.g.f.: (1 - x + x^2)*exp((1 + x + x^2)*t)/((1 + x^2)*exp(2*t*x) - x*exp(2*(1 + x^2)*t)). - Franck Maminirina Ramaharo, Oct 25 2018

Extensions

Edited, new name, and offset corrected by Franck Maminirina Ramaharo, Oct 25 2018