%I #14 Sep 08 2022 08:44:52

%S 0,1,17,125,637,2637,9549,31501,97037,283661,795661,2158605,5697549,

%T 14696461,37175309,92471309,226689037,548667405,1313079309,3111125005,

%U 7305429005,17016291341,39346765837,90378862605,206342979597,468486979597,1058239676429

%N A036827/2.

%C This sequence is related to A036826 by a(n) = n*A036826(n)-sum(A036826(i), i=0..n-1). - Bruno Berselli, Mar 06 2012

%H Bruno Berselli, <a href="/A036828/b036828.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (9,-32,56,-48,16).

%F G.f.: -x*(4*x^2+8*x+1)/((x-1)*(2*x-1)^4). [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 13 2009]

%F a(n) = 2^n*(n^3-3*n^2+9*n-13)+13. - Bruno Berselli, Mar 06 2012

%t LinearRecurrence[{9, -32, 56, -48, 16}, {0, 1, 17, 125, 637}, 27] (* _Bruno Berselli_, Mar 06 2012 *)

%o (Magma) m:=26; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(-(4*x^2+8*x+1)/((x-1)*(2*x-1)^4))); // Bruno Berselli, Mar 06 2012

%o (PARI) for(n=0, 26, print1(2^n*(n^3-3*n^2+9*n-13)+13", ")); \\ Bruno Berselli, Mar 06 2012

%Y Cf. A036826, A209359.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_.

%E Typo in definition corrected by R. J. Mathar, Sep 16 2009