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.

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A138175 Row sums of the Riordan array (1/(1+x),x(1+2x)/(1+x)^3)^(-1).

Original entry on oeis.org

1, 2, 4, 10, 24, 62, 156, 408, 1048, 2758, 7164, 18922, 49488, 131016, 344208, 912720, 2405496, 6385814, 16868604, 44818494, 118595064, 315299694, 835423164, 2222185344, 5894038944, 15684059112
Offset: 0

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Author

Paul Barry, Mar 03 2008

Keywords

Comments

A transform of 2^n by the Riordan array (1,x(1-x^2))^(-1).
(1/(1+x),x(1+2x)/(1+x)^3)^(-1) factors as (1,x(1-x^2))^(-1)*(1/(1-x),x/(1-x)).
Hankel transform is A138176.

Formula

G.f.: 1/(1-2v) where v=(2/sqrt(3))*sin(asin(x*3*sqrt(3)/2)/3), the reversion of x(1-x^2);
Conjecture: 12*n*(n-1)*(39*n-88)*a(n) -8*(n-1)*(156*n^2-352*n+27)*a(n-1) +9*(-351*n^3-2196*n^2-4325*n+2680)*a(n-2) +24*(39*n-49)*(3*n-7)*(3*n-8)*a(n-3)=0.- R. J. Mathar, Oct 25 2012
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