A084266 Binomial transform of A084265.

1, 3, 11, 34, 96, 256, 656, 1632, 3968, 9472, 22272, 51712, 118784, 270336, 610304, 1368064, 3047424, 6750208, 14876672, 32636928, 71303168, 155189248, 336592896, 727711744, 1568669696, 3372220416, 7230980096, 15468593152, 33017561088

Offset: 0

Author

Paul Barry, May 31 2003

Keywords

• easy
• nonn

Comments

The sequence starting with a(1) is the binomial transform of A005563 starting with A005563(1). - Paul Curtz, Jan 02 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Programs

Magma

[0^n/2+2^n*(n^2+7*n+4)/8: n in [0..35]]; // Vincenzo Librandi, Aug 13 2011

Mathematica

LinearRecurrence[{6,-12,8},{1,3,11,34},30] (* Harvey P. Dale, Dec 12 2021 *)

Formula

E.g.f.: exp(x)*cosh(x) + exp(2*x)*(2*x+x^2/2); a(n) = 0^n/2 + 2^n*(n^2 + 7*n + 4)/8.

a(n) = Sum_{k=0..n-1} a(k) + (n+2)*2^(n-1) - 1. - Philippe Deléham, Jul 12 2007

G.f.: (-4 + 13*x - 16*x^2 + 8*x^3)/(2*x-1)^3. - R. J. Mathar, Jan 06 2011

a(n) = (Sum_{k=0..n+1} binomial(n+1,k)*k^4)/((n+1)*(n+2)), n > 0. - Gary Detlefs, Nov 26 2011