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

0,2

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).

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A004662 A247103 A036542 * A357592 A052471 A037496

Adjacent sequences: A084263 A084264 A084265 * A084267 A084268 A084269

Keyword

easy,nonn

Author

Paul Barry, May 31 2003

Status

approved