A081893 Third binomial transform of C(n+2,2).

1, 6, 33, 172, 864, 4224, 20224, 95232, 442368, 2031616, 9240576, 41680896, 186646528, 830472192, 3674210304, 16173236224, 70866960384, 309237645312, 1344324763648, 5823975653376, 25151328485376, 108301895335936

Offset: 0

Author

Paul Barry, Mar 30 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A081892.

3rd binomial transform of C(n+2,2), A000217.

4th binomial transform of (1,2,1,0,0,0,.....)

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-48,64).

Crossrefs

Cf. A081894.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^2/(1-4*x)^3)); // G. C. Greubel, Oct 18 2018

Mathematica

LinearRecurrence[{12, -48, 64}, {1, 6, 33}, 50] (* G. C. Greubel, Oct 18 2018 *)

PARI

x='x+O('x^30); Vec((1-3*x)^2/(1-4*x)^3) \\ G. C. Greubel, Oct 18 2018

Formula

a(n) = 4^n*(n^2 + 15*n + 32)/32.

G.f.: (1 - 3*x)^2/(1 - 4*x)^3.

E.g.f.: (2 + 4*x + x^2)*exp(4*x)/2. - G. C. Greubel, Oct 18 2018