A119635 a(n) = n*(1 + n^2)*2^n.

4, 40, 240, 1088, 4160, 14208, 44800, 133120, 377856, 1034240, 2748416, 7127040, 18104320, 45187072, 111083520, 269484032, 646184960, 1533542400, 3606052864, 8409579520, 19465764864, 44753223680, 102257131520, 232330887168

Offset: 1

Author

Mohammad K. Azarian, May 02 2007

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Crossrefs

Cf. A128796, A128960, A128985, A129002.

Programs

GAP

List([1..30],n->n*(n^2+1)*2^n); # Muniru A Asiru, Mar 04 2019

Magma

[(n^3 + n)*2^n: n in [1..30]]; // Vincenzo Librandi, Feb 22 2013

Maple

[(n^3+n)*2^n$n=1..30]; # Muniru A Asiru, Mar 04 2019

Mathematica

Table[(n^3 + n)*2^n, {n, 30}] (* or *) CoefficientList[Series[4(1 +2x + 4x^2)/(1-2x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)

PARI

{a(n) = n*(1+n^2)*2^n}; \\ G. C. Greubel, Mar 04 2019

Sage

[n*(1+n^2)*2^n for n in (1..30)] # G. C. Greubel, Mar 04 2019

Formula

G.f.: 4*x*(1 + 2*x + 4*x^2)/(1 - 2*x)^4. - Vincenzo Librandi, Feb 22 2013

E.g.f.: 4*x*(1 + 3*x + 2*x^2)*exp(2*x). - G. C. Greubel, Mar 04 2019