A105938 a(n) = binomial(n+2,2)*binomial(n+5,2).

10, 45, 126, 280, 540, 945, 1540, 2376, 3510, 5005, 6930, 9360, 12376, 16065, 20520, 25840, 32130, 39501, 48070, 57960, 69300, 82225, 96876, 113400, 131950, 152685, 175770, 201376, 229680, 260865, 295120, 332640, 373626, 418285, 466830, 519480, 576460

Offset

0,1

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..5000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: (x^2-5*x+10)/(1-x)^5. - Alois P. Heinz, Oct 16 2008

a(0)=10, a(1)=45, a(2)=126, a(3)=280, a(4)=540; for n>4, a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Harvey P. Dale, Sep 05 2013

a(n) = A000217(n+1)*A000217(n+4). - R. J. Mathar, Nov 29 2015

a(n) = A000096(n+1)*A000096(n+2). - Bruno Berselli, Sep 21 2016

From Amiram Eldar, Jan 06 2021: (Start)

Sum_{n>=0} 1/a(n) = 5/36.

Sum_{n>=0} (-1)^n/a(n) = 1/12. (End)

Example

If n=0 then C(0+2,0)*C(0+5,2) = C(2,0)*C(5,2) = 1*10 = 10.
If n=9 then C(9+2,9)*C(9+5,2) = C(11,9)*C(14,2) = 55*91 = 5005.

Maple

a:= n-> binomial(n+2, n)*binomial(n+5, 2):
seq(a(n), n=0..40);  # Alois P. Heinz, Oct 16 2008

Mathematica

Table[n (n + 1) (n + 3) (n + 4)/4, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
Table[Binomial[n + 2, n] Binomial[n + 5, 2], {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {10, 45, 126, 280, 540}, 40] (* Harvey P. Dale, Sep 05 2013 *)

Crossrefs

Subsequence of A085780.

Cf. A000096, A000217, A062145.

Sequence in context: A306965 A045852 A226450 * A342254 A226254 A340966

Adjacent sequences: A105935 A105936 A105937 * A105939 A105940 A105941

Keyword

nonn,easy

Author

Zerinvary Lajos, Apr 27 2005

Status

approved