A051746 a(n) = n(n+7)(n+1)(n^2+2n+12)/120.

2, 9, 27, 66, 141, 273, 490, 828, 1332, 2057, 3069, 4446, 6279, 8673, 11748, 15640, 20502, 26505, 33839, 42714, 53361, 66033, 81006, 98580, 119080, 142857, 170289, 201782, 237771, 278721, 325128, 377520, 436458, 502537, 576387, 658674, 750101

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000 (Corrected by Alois P. Heinz, Mar 14 2016)

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = binomial(n+4, n-1)+binomial(n+1, n-1).

G.f.: x*(2-x)*(1-x+x^2)/(1-x)^6. - Colin Barker, Mar 19 2012

Mathematica

Table[1/120*n*(n + 7)*(n + 1)*(n^2 + 2*n + 12), {n, 60}] (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {2, 9, 27, 66, 141, 273}, 40] (* Harvey P. Dale, Apr 28 2018 *)

Prog

(PARI) a(n)=((((n+10)*n+35)*n+110)*n+84)*n/120 \\ Charles R Greathouse IV, Jun 14 2011
(Magma) [1/120*n*(n+7)*(n+1)*(n^2+2*n+12): n in [1..50]]; // Vincenzo Librandi, Jun 15 2011

Crossrefs

Sequence in context: A008910 A239059 A153977 * A277240 A256233 A123904

Adjacent sequences: A051743 A051744 A051745 * A051747 A051748 A051749

Keyword

easy,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 07 1999

Status

approved