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A063267 Eighth column (k=7) of septinomial array A063265.

%I A063267 #13 Feb 23 2019 19:38:11
%S A063267 6,33,116,325,786,1709,3424,6426,11430,19437,31812,50375,77506,116265,
%T A063267 170528,245140,346086,480681,657780,888009,1184018,1560757,2035776,
%U A063267 2629550,3365830,4272021,5379588,6724491,8347650
%N A063267 Eighth column (k=7) of septinomial array A063265.
%H A063267 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8, -28, 56, -70, 56, -28, 8, -1).
%F A063267 a(n)= A063265(n+2, 7)= (n+1)*(n+2)*(n+10)*(n^4 + 22*n^3 + 193*n^2 + 792*n + 1512)/7!.
%F A063267 G.f.: (2-x)*(1-x+x^2)*(3-3*x+x^2)/(1-x)^8; the numerator polynomial is N7(7, x) = 6 - 15*x + 20*x^2 - 15*x^3 + 6*x^4 - x^5 from row n=7 of array A063266.
%F A063267 a(n) = binomial(n+7,n) - binomial(n+1,n). - _Zerinvary Lajos_, Jun 23 2006
%F A063267 a(n) = binomial(n+7,n) + binomial(n+6,n) + binomial(n+5,n) + binomial(n+4,n) + binomial(n+3,n) + binomial(n+2,n). - _Zerinvary Lajos_, Jun 23 2006
%F A063267 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8); a(0)=6, a(1)=33, a(2)=116, a(3)=325, a(4)=786, a(5)=1709, a(6)=3424, a(7)=6426. - _Harvey P. Dale_, Jan 06 2012
%p A063267 [seq((binomial(n+7,n)-binomial(n+1,n)),n=1..29)]; # _Zerinvary Lajos_, Jun 23 2006
%t A063267 Table[Binomial[n+7,n]-Binomial[n+1,n],{n,30}] (* or *) LinearRecurrence[ {8,-28,56,-70,56,-28,8,-1},{6,33,116,325,786,1709,3424,6426},30] (* _Harvey P. Dale_, Jan 06 2012 *)
%Y A063267 Cf. A000579 (column k=6 of A063265).
%K A063267 nonn,easy
%O A063267 0,1
%A A063267 _Wolfdieter Lang_, Jul 24 2001
%E A063267 More terms from _Zerinvary Lajos_, Jun 23 2006