OFFSET
0,2
COMMENTS
With two initial 0, convolution of the oblong numbers (A002378) with the nonnegative even numbers (A005843). - Bruno Berselli, Oct 24 2016
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..700
FORMULA
a(n) = n*C(3+n, 3). - Zerinvary Lajos, Jan 10 2006
G.f.: 4*x/(1-x)^5. - Colin Barker, Mar 01 2012
G.f.: 2*x/(1-x)*W(0), where W(k) = 1 + 1/( 1 - x*(k+2)*(k+4)/(x*(k+2)*(k+4) + (k+1)*(k+2)/W(k+1) )) ); (continued fraction). - Sergei N. Gladkovskii, Aug 24 2013
From Amiram Eldar, Jun 02 2022: (Start)
Sum_{n>=1} 1/a(n) = 1/3.
Sum_{n>=1} (-1)^(n+1)/a(n) = 8*log(2) - 16/3. (End)
MAPLE
[seq(4*binomial(n+3, 4), n=0..35)]; # Zerinvary Lajos, Nov 24 2006
MATHEMATICA
f[n_]:=n*(n+1)*(n+2)*(n+3)/6; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 21 2009 *)
# Binomial[#+3, 3]&/@ Range[0, 40] (* Harvey P. Dale, Feb 20 2011 *)
PROG
(Magma) [n*(n+1)*(n+2)*(n+3)/6: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
(Maxima) A033488(n):=n*(n+1)*(n+2)*(n+3)/6$ makelist(A033488(n), n, 0, 20); /* Martin Ettl, Jan 22 2013 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved