A086030 a(n) = Sum_{i=1..n} C(i+6,7)^3.

1, 513, 47169, 1775169, 37712169, 534505257, 5587534953, 46011772521, 312480135396, 1809674119396, 9165388162788, 41395684407012, 169328324418084, 635173167426084, 2207399512578084, 7167715400927268, 21902130296812161, 63361228916945025, 174437774859945025

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

a(n) = C(n+7,8)*(5*C(n+13,14) + 210*C(n+12,14) + 1491*C(n+11,14) + 2828*C(n+10,14) + 1491*C(n+9,14) + 210*C(n+8,14) + 5*C(n+7,14))/5. - Yahia Kahloune, Dec 22 2013

-(n-1)^3*a(n) +(2*n+5)*(n^2+5*n+43)*a(n-1) -(n+6)^3*a(n-2)=0. - R. J. Mathar, Dec 22 2013

G.f.: -x*(x^14 + 490*x^13 + 35623*x^12 + 818300*x^11 + 7917371*x^10 + 37215794*x^9 + 91789005*x^8 + 123519792*x^7 + 91789005*x^6 + 37215794*x^5 + 7917371*x^4 + 818300*x^3 + 35623*x^2 + 490*x + 1)/(x-1)^23. - Vaclav Kotesovec, Dec 23 2013

a(n) = (1/28165294080000)*n^2*(1 + n)^2*(2 + n)^2*(3 + n)^2*(4 + n)^2*(5 + n)^2*(6 + n)^2*(7 + n)^2*(-3 + 3234*n + 6979*n^2 + 5292*n^3 + 1603*n^4 + 210*n^5 + 10*n^6). - G. C. Greubel, Nov 22 2017

Example

a(3) = Sum_{i=1..3} C(6+i,7)^3 = C(10,8)*(5*C(16,14) + 210*C(15,14) + 1491*C(14,14))/5 = 47169.

Maple

A086030:=n->add(binomial(i+6, 7)^3, i=1..n); seq(A086030(n), n=1..30); # Wesley Ivan Hurt, Dec 22 2013

Mathematica

Table[Sum[Binomial[i + 6, 7]^3, {i, n}], {n, 30}] (* Wesley Ivan Hurt, Dec 22 2013 *)

Prog

(PARI) a(n) = sum(i=1, n, binomial(i+6, 7)^3); \\ Michel Marcus, Dec 22 2013
(Magma) [(1/28165294080000)*n^2*(1 + n)^2*(2 + n)^2*(3 + n)^2*(4 + n)^2*(5 + n)^2*(6 + n)^2*(7 + n)^2*(-3 + 3234*n + 6979*n^2 + 5292*n^3 + 1603*n^4 + 210*n^5 + 10*n^6): n in [1..30]]; // G. C. Greubel, Nov 22 2017

Crossrefs

Cf. A087127, A024166, A085438 - A085442, A086020 - A086029.

Sequence in context: A297494 A279642 A168118 * A094647 A236431 A118709

Adjacent sequences: A086027 A086028 A086029 * A086031 A086032 A086033

Keyword

easy,nonn

Author

André F. Labossière, Jul 11 2003

Status

approved