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

0,2

Comments

Partial sums of A166696.

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(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

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 *)

Crossrefs

Cf. A085478, A103210, A166696

Sequence in context: A367017 A370473 A369479 * A054368 A365764 A135147

Adjacent sequences: A166694 A166695 A166696 * A166698 A166699 A166700

Keyword

easy,nonn

Author

Paul Barry, Oct 18 2009

Status

approved