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A086021 a(n) = Sum_{i=1..n} C(i+2,3)^3. 20
1, 65, 1065, 9065, 51940, 227556, 820260, 2548260, 7040385, 17688385, 41082041, 89310585, 183506960, 359122960, 673554960, 1216893456, 2126746665, 3608290665, 5960927665, 9613191665, 15167828676, 23459298500, 35626298500, 53202298500, 78227501625, 113386110201 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = (C(n+3, 4)/1)*(1 +12*C(n-1, 1) +46*C(n-1, 2) +84*C(n-1, 3) +81*C(n-1, 4) +40*C(n-1, 5) +8*C(n-1, 6)). - Edited by Colin Barker, May 02 2014
G.f.: -x*(x^6 +54*x^5 +405*x^4 +760*x^3 +405*x^2 +54*x +1) / (x-1)^11. - Colin Barker, May 02 2014
a(n) = n^2*(-36 + 300*n + 1535*n^2 + 2700*n^3 + 2442*n^4 + 1260*n^5 + 375*n^6 + 60*n^7 + 4*n^8)/8640. - G. C. Greubel, Nov 22 2017
MATHEMATICA
Table[n^2*(-36 + 300*n + 1535*n^2 + 2700*n^3 + 2442*n^4 + 1260*n^5 + 375*n^6 + 60*n^7 + 4*n^8)/8640, {n, 1, 30}] (* G. C. Greubel, Nov 22 2017 *)
PROG
(PARI) Vec(-x*(x^6+54*x^5+405*x^4+760*x^3+405*x^2+54*x+1)/(x-1)^11 + O(x^100)) \\ Colin Barker, May 02 2014
(PARI) for(n=1, 30, print1(n^2*(-36 + 300*n + 1535*n^2 + 2700*n^3 + 2442*n^4 + 1260*n^5 + 375*n^6 + 60*n^7 + 4*n^8)/8640, ", ")) \\ G. C. Greubel, Nov 22 2017
(Magma) [n^2*(-36 + 300*n + 1535*n^2 + 2700*n^3 + 2442*n^4 + 1260*n^5 + 375*n^6 + 60*n^7 + 4*n^8)/8640: n in [1..30]]; // G. C. Greubel, Nov 22 2017
CROSSREFS
Sequence in context: A305264 A279639 A144500 * A168029 A219413 A069424
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified February 21 10:12 EST 2024. Contains 370228 sequences. (Running on oeis4.)