A086026 a(n) = Sum_{i=1..n} C(i+4,5)^3.

1, 217, 9478, 185094, 2185470, 18188478, 116799606, 613592694, 2745339597, 10769363605, 37850444632, 121189368664, 358136205336, 987118431768, 2559344776920, 6286103520984, 14712254089533, 32974344717237, 71073599975686, 147860902015750, 297836101312750

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376, 19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Formula

a(n) = C(n+5,6)^2*(1 + 279*C(n,1) + 681*C(n,2) + 504*C(n,3) + 126*C(n,4) )/280. - Yahia Kahloune, Dec 22 2013

-(n-1)^3*a(n) +(2*n+3)*(n^2+3*n+21)*a(n-1) -(n+4)^3*a(n-2)=0. - R. J. Mathar, Dec 22 2013

G.f.: -x*(x^10 +200*x^9 +5925*x^8 +52800*x^7 +182700*x^6 +273504*x^5 +182700*x^4 +52800*x^3 +5925*x^2 +200*x +1) / (x -1)^17. - Colin Barker, May 02 2014

a(n) = (n^2/580608000)*(57600 + 4583040*n + 28668304*n^2 + 80791200*n^3 + 133134680*n^4 + 142979760*n^5 + 105929613*n^6 + 55881000*n^7 + 21323540* n^8 + 5904360*n^9 + 1175062*n^10 + 163800*n^11 + 15180*n^12 + 840*n^13 + 21*n^14). - G. C. Greubel, Nov 22 2017

Example

a(3) = C(8,6)^2*(1 + 279*C(3,1) + 681*C(3,2) + 504*C(3,3))/280 = 9478. - Yahia Kahloune, Dec 22 2013

Maple

A086026 := proc(n)
    add( binomial(i+4, 5)^3, i=1..n) ;
end proc:
seq(A086026(n), n=1..30) ; # R. J. Mathar, Dec 22 2013

Mathematica

Table[Sum[Binomial[i + 4, 5]^3, {i, n}], {n, 30}] (* Wesley Ivan Hurt, Dec 22 2013 *)

Prog

(PARI) a(n) = sum(i=1, n, binomial(i+4, 5)^3); \\ Michel Marcus, Dec 22 2013
(Magma) [(n^2/580608000)*(57600 + 4583040*n + 28668304*n^2 + 80791200*n^3 + 133134680*n^4 + 142979760*n^5 + 105929613*n^6 + 55881000*n^7 + 21323540* n^8 + 5904360*n^9 + 1175062*n^10 + 163800*n^11 + 15180*n^12 + 840*n^13 + 21*n^14): n in [1..30]]; // G. C. Greubel, Nov 22 2017

Crossrefs

Cf. A087127, A024166, A085438 - A085442, A086020 - A086030.

Sequence in context: A183778 A250448 A221427 * A100794 A048258 A013541

Adjacent sequences: A086023 A086024 A086025 * A086027 A086028 A086029

Keyword

easy,nonn

Author

André F. Labossière, Jul 11 2003

Extensions

More terms from Michel Marcus, Dec 22 2013

Status

approved