A188589 Expansion of (1-3*x+6*x^2-3*x^3)/((1-x)^2*(1-2*x)).

1, 1, 5, 14, 33, 72, 151, 310, 629, 1268, 2547, 5106, 10225, 20464, 40943, 81902, 163821, 327660, 655339, 1310698, 2621417, 5242856, 10485735, 20971494, 41943013, 83886052, 167772131, 335544290, 671088609, 1342177248, 2684354527

Offset: 0

Author

Paul Barry, Apr 04 2011

Keywords

• nonn
• easy

Comments

Second column of the 1-Euler triangle A188587. In general, the second column of the r-Euler triangle has g.f. (1-(4-r)*x+2*(4-r)*x^2-(4-r)*x^3)/((1-x)^2*(1-2*x)).

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Programs

Mathematica

CoefficientList[Series[(1-3x+6x^2-3x^3)/((1-x)^2(1-2x)),{x,0,30}],x] (* or *) LinearRecurrence[{4,-5,2},{1,1,5,14},40] (* Harvey P. Dale, Nov 26 2017 *)

PARI

a(n) = if (n==0, 1, 5*2^(n-1) - n - 3) \\ Michel Marcus, Jul 24 2013

Formula

a(n+1)=A094002(n).

a(n) = 5*2^(n-1)-n-3, n>0.