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(2^n+1)*(2^n+2)*(2^n+4)*(2^n+6)*(4^n+15*2^n+176)/8!.
0

%I #13 Jul 31 2015 10:40:27

%S 1,3,15,135,2244,63954,2649790,135954390,7791419142,471957819750,

%T 29387888461350,1855241125539750,117925810919637670,

%U 7521488030252902566,480553086854453064870,30729125540385201818790,1965823916539674220608678

%N (2^n+1)*(2^n+2)*(2^n+4)*(2^n+6)*(4^n+15*2^n+176)/8!.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (127, -5334, 94488, -755904, 2731008, -4161536, 2097152).

%F a(0)=1, a(1)=3, a(2)=15, a(3)=135, a(4)=2244, a(5)=63954, a(6)=2649790, a(n)=127*a(n-1)-5334*a(n-2)+94488*a(n-3)-755904*a(n-4)+ 2731008*a(n-5)- 4161536*a(n-6)+2097152*a(n-7). - _Harvey P. Dale_, Jun 17 2011

%F G.f.: (-1+x*(124-3*x*(1656+x*(-26752+x*(179183+40*x*(-11513+8736*x))))))/ ((-1+x)(-1+2*x)(-1+4*x)(-1+8*x)(-1+16*x)(-1+32*x)*(-1+64*x)). - _Harvey P. Dale_, Jun 17 2011

%t LinearRecurrence[{127,-5334,94488,-755904,2731008,-4161536,2097152}, {1,3,15,135,2244,63954,2649790},20] (* or *) Table[(2^n+1)(2^n+2) (2^n+4) (2^n+6)(4^n+15 2^n+176)/8!,{n,0,20}] (* _Harvey P. Dale_, Jun 17 2011 *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_