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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..500
Programs
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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
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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 *)
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
Extensions
A-number in formula corrected by R. J. Mathar, Feb 10 2015
Comments