A081913 a(n) = 2^n*(n^3 - 3n^2 + 2n + 48)/48.

1, 2, 4, 9, 24, 72, 224, 688, 2048, 5888, 16384, 44288, 116736, 301056, 761856, 1896448, 4653056, 11272192, 27000832, 64028672, 150470656, 350748672, 811597824, 1865416704, 4261412864, 9680453632, 21877489664, 49207574528

Offset: 0

Author

Paul Barry, Mar 31 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A050407, (starting with 1,1,1,2,5,...). 2nd binomial transform of (1,0,0,1,0,0,0,0,...). Case k=2 where a(n,k) = k^n*(n^3 - 3n^2 + 2n + 6k^3)/(6k^3), with g.f. (1 - 3kx + 3k^2x^2 - (k^3-1)x^3)/(1-kx)^4.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..225
• Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Crossrefs

Cf. A081914.

Programs

Magma

[2^n*(n^3-3*n^2+2*n+48)/48: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

Formula

a(n) = 2^n*(n^3 - 3n^2 + 2n + 48)/48.

G.f.: (1 - 6x + 12x^2 - 7x^3)/(1-2x)^4.