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 A084266 Binomial transform of A084265. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 6 03:16 EDT 2024. Contains 374957 sequences. (Running on oeis4.)