A166696 A transform of A103210.

1, 3, 21, 162, 1365, 12219, 114156, 1100649, 10871175, 109438830, 1118798079, 11583712617, 121219182504, 1280065637487, 13623341795049, 145977237305874, 1573536198376401, 17051418418204671, 185646639499541892

Offset

0,2

Comments

Partial sums are A166697.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

G.f.: (1-3x+x^2-sqrt(1-14x+27x^2-14x^3+x^4))/(4x);

G.f.: 1/(1-3x/((1-x)^2-2x/(1-3x/((1-x)^2-2x/(1-3x/((1-x)^2-2x/(1-3x/(1-... (continued fraction);

a(n) = Sum_{k=0..n} (0^(n+k)+C(n+k-1,2k-1))*A103210(k) = 0^n + Sum_{k=0..n} C(n+k-1,2k-1)*A103210(k).

Conjecture: (n+1)*a(n) +7*(-2*n+1)*a(n-1) +27*(n-2)*a(n-2) +7*(-2*n+7)*a(n-3) +(n-5)*a(n-4)=0. - R. J. Mathar, Feb 10 2015

Maple

A166696 := proc(n)
    if n = 0 then
        1;
    else
        add((0^(n+k)+binomial(n+k-1, 2*k-1))*A103210(k), k=0..n) ;
    end if;
end proc: # R. J. Mathar, Feb 10 2015

Mathematica

CoefficientList[Series[(1 - 3*t + t^2 - Sqrt[1 - 14*t + 27*t^2 - 14*t^3 + t^4])/(4*t), {t, 0, 50}], t] (* G. C. Greubel, May 23 2016 *)

Crossrefs

Sequence in context: A136781 A225439 A180400 * A058194 A179815 A118353

Adjacent sequences: A166693 A166694 A166695 * A166697 A166698 A166699

Keyword

easy,nonn

Author

Paul Barry, Oct 18 2009

Extensions

A-number in formula corrected by R. J. Mathar, Feb 10 2015

Status

approved