Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Feb 18 2024 17:44:56
%S 1,126,3501,46376,389376,2389752,11650752,47587752,168875127,
%T 534401002,1537404003,4080706128,10109274128,23590546128,52243162128,
%U 110473767504,224205418629,438589465254,830009446129,1524339072504,2724140666880,4748425291880,8089787666880
%N a(n) = Sum_{i=1..n} C(i+3,4)^3.
%H T. D. Noe, <a href="/A086024/b086024.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14,-91,364,-1001,2002,-3003,3432, -3003,2002,-1001,364,-91,14,-1).
%F a(n) = ( C(n+4, 5)/1001 )*( 1001 +20020*C(n-1, 1) +125840*C(n-1, 2) +390390*C(n-1, 3) +695695*C(n-1, 4) +750750*C(n-1, 5) +486850*C(n-1, 6) +175175*C(n-1, 7) +26950*C(n-1, 8) ).
%F G.f.: x*(1 +112*x +1828*x^2 +8464*x^3 +13840*x^4 +8464*x^5 +1828*x^6 +112*x^7 +x^8)/(x-1)^14 . - _R. J. Mathar_, Dec 22 2013
%F -(n-1)^3*a(n) +2*(n+1)*(n^2+2*n+13)*a(n-1) -(n+3)^3*a(n-2)=0. - _R. J. Mathar_, Dec 22 2013
%F a(n) = (n/69189120)*(13824 + 960960*n^2 + 5885880*n^3 + 14370356*n^4 + 19269250*n^5 + 15996695*n^6 + 8678670*n^7 + 3138135*n^8 + 750750*n^9 + 114205*n^10 + 10010*n^11 + 385*n^12). - _G. C. Greubel_, Nov 22 2017
%t Table[(n/69189120)*(13824 + 960960*n^2 + 5885880*n^3 + 14370356*n^4 + 19269250*n^5 + 15996695*n^6 + 8678670*n^7 + 3138135*n^8 + 750750*n^9 + 114205*n^10 + 10010*n^11 + 385*n^12), {n,1,30}] (* _G. C. Greubel_, Nov 22 2017 *)
%t LinearRecurrence[{14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1},{1,126,3501,46376,389376,2389752,11650752,47587752,168875127,534401002,1537404003,4080706128,10109274128,23590546128},30] (* _Harvey P. Dale_, Feb 18 2024 *)
%o (PARI) for(n=1,30, print1(sum(k=1,n, binomial(k+3, 4)^3), ", ")) \\ _G. C. Greubel_, Nov 22 2017
%o (Magma) [(n/69189120)*(13824 + 960960*n^2 + 5885880*n^3 + 14370356*n^4 + 19269250*n^5 + 15996695*n^6 + 8678670*n^7 + 3138135*n^8 + 750750*n^9 + 114205*n^10 + 10010*n^11 + 385*n^12): n in [1..30]]; // _G. C. Greubel_, Nov 22 2017
%Y Cf. A087127, A024166, A085438 - A085442, A086020 - A086030.
%K easy,nonn
%O 1,2
%A _André F. Labossière_, Jul 11 2003