A166697 A "Morgan Voyce" transform of A103210.

1, 4, 25, 187, 1552, 13771, 127927, 1228576, 12099751, 121538581, 1240336660, 12824049277, 134043231781, 1414108869268, 15037450664317, 161014687970191, 1734550886346592, 18785969304551263, 204432608804093155

Offset: 0

Author

Paul Barry, Oct 18 2009

Keywords

• easy
• nonn

Comments

Partial sums of A166696.

Links

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

Crossrefs

Cf. A085478, A103210, A166696

Programs

Maple

A166697 := proc(n)
    add(A166696(k),k=0..n) ;
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*(1 - 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(1-x));

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

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

a(n) = Sum_{k=0..n} A085478(n,k)*A103210(k). - Philippe Deléham, Nov 16 2013

Conjecture: (n+1)*a(n) + 3*(-5*n+2)*a(n-1) + (41*n-61)*a(n-2) + (-41*n+103)*a(n-3) + 3*(5*n-18)*a(n-4) + (-n+5)*a(n-5) = 0. - R. J. Mathar, Feb 10 2015