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.

A186341 a(n)=sum{k=0..floor(n/2), binomial(n-k,k)*A186338(k)}.

Original entry on oeis.org

1, 1, 3, 5, 15, 33, 95, 237, 667, 1765, 4943, 13505, 37967, 105837, 299675, 847253, 2417903, 6909409, 19866303, 57253165, 165728475, 480938693, 1400391247, 4087481409, 11963060527, 35089773869, 103157489499, 303856951925, 896755068783, 2651120922081, 7850714948511
Offset: 0

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Author

Paul Barry, Feb 18 2011

Keywords

Comments

Hankel transform is A134751.

Programs

  • Mathematica
    CoefficientList[Series[(1-x-3x^2-Sqrt[(1-3x-7x^2+19x^3+15x^4-25x^5-16x^6)/(1-x)])/(2x^2(1-x-2x^2)),{x,0,40}],x]  (* Harvey P. Dale, Mar 04 2011 *)

Formula

G.f.: 1/(1-x-2x^2/(1-2x^2/(1-x-x^2/(1-2x^2/(1-x-2x^2/(1-x^2/(1-x-2x^2/(1-... (continued fraction).
G.f.: (1-x-3x^2-sqrt((1-3x-7x^2+19x^3+15x^4-25x^5-16x^6)/(1-x)))/(2x^2(1-x-2x^2)).
Conjecture: (n+2)*a(n) +5*(-n-1)*a(n-1) +2*(-n+3)*a(n-2) +(38*n-59)*a(n-3) +(-22*n+41)*a(n-4) +4*(-22*n+81)*a(n-5) +3*(19*n-79)*a(n-6) +3*(29*n-164)*a(n-7) +2*(-17*n+98)*a(n-8) +16*(-2*n+15)*a(n-9)=0. - R. J. Mathar, Oct 08 2016