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%I #34 Sep 08 2022 08:45:11
%S 1,3,11,34,96,256,656,1632,3968,9472,22272,51712,118784,270336,610304,
%T 1368064,3047424,6750208,14876672,32636928,71303168,155189248,
%U 336592896,727711744,1568669696,3372220416,7230980096,15468593152,33017561088
%N Binomial transform of A084265.
%C The sequence starting with a(1) is the binomial transform of A005563 starting with A005563(1). - _Paul Curtz_, Jan 02 2011
%H Vincenzo Librandi, <a href="/A084266/b084266.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F 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.
%F a(n) = Sum_{k=0..n-1} a(k) + (n+2)*2^(n-1) - 1. - _Philippe Deléham_, Jul 12 2007
%F G.f.: (-4 + 13*x - 16*x^2 + 8*x^3)/(2*x-1)^3. - _R. J. Mathar_, Jan 06 2011
%F a(n) = (Sum_{k=0..n+1} binomial(n+1,k)*k^4)/((n+1)*(n+2)), n > 0. - _Gary Detlefs_, Nov 26 2011
%t LinearRecurrence[{6,-12,8},{1,3,11,34},30] (* _Harvey P. Dale_, Dec 12 2021 *)
%o (Magma) [0^n/2+2^n*(n^2+7*n+4)/8: n in [0..35]]; // _Vincenzo Librandi_, Aug 13 2011
%K easy,nonn
%O 0,2
%A _Paul Barry_, May 31 2003
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