%I #8 Sep 20 2022 19:19:44
%S 1,9,55,295,1510,7606,38114,190690,953615,4768295,23841761,119209169,
%T 596046300,2980232060,14901160980,74505805716,372529029549,
%U 1862645148885,9313225745755,46566128730315,232830643653346
%N a(n)=5a(n-1)+C(n+3,3),n>0, a(0)=1.
%C Partial sums of A052244.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,34,-21,5).
%F G.f. : 1/((1-5x)(1-x)^4)); a(n)=5^(n+4)/256-(32n^3+312n^2+1012n+1107)/768; a(n)=sum{k=0..n, binomial(n+4, k+4)4^k }.
%t nxt[{n_,a_}]:={n+1,5a+Binomial[n+4,3]}; NestList[nxt,{0,1},20][[All,2]] (* or *) LinearRecurrence[{9,-26,34,-21,5},{1,9,55,295,1510},30] (* _Harvey P. Dale_, Sep 20 2022 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Aug 24 2004
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