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A086024
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a(n) = Sum_{i=1..n} C(i+3,4)^3.
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21
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1, 126, 3501, 46376, 389376, 2389752, 11650752, 47587752, 168875127, 534401002, 1537404003, 4080706128, 10109274128, 23590546128, 52243162128, 110473767504, 224205418629, 438589465254, 830009446129, 1524339072504, 2724140666880, 4748425291880, 8089787666880
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OFFSET
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1,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432, -3003,2002,-1001,364,-91,14,-1).
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FORMULA
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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) ).
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
-(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
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
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MATHEMATICA
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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 *)
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 *)
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PROG
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(PARI) for(n=1, 30, print1(sum(k=1, n, binomial(k+3, 4)^3), ", ")) \\ G. C. Greubel, Nov 22 2017
(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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