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A097791 a(n)=5a(n-1)+C(n+4,4),n>0, a(0)=1.

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%I A097791 #9 Aug 29 2024 21:13:06
%S A097791 1,10,65,360,1870,9476,47590,238280,1191895,5960190,29801951,
%T A097791 149011120,745057420,3725289480,18626450460,93132256176,465661285725,
%U A097791 2328306434610,11641532180365,58207660910680,291038304564026
%N A097791 a(n)=5a(n-1)+C(n+4,4),n>0, a(0)=1.
%C A097791 Partial sums of A097790.
%H A097791 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,60,-55,26,-5).
%F A097791 G.f.: 1/((1-5*x)*(1-x)^5).
%F A097791 a(n) = 5^(n+5)/1024-(32*n^4+480*n^3+2680*n^2+6660*n+6303)/3072.
%F A097791 a(n) = Sum_{k=0..n} binomial(n+5, k+5)*4^k.
%K A097791 easy,nonn
%O A097791 0,2
%A A097791 _Paul Barry_, Aug 24 2004