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 A033488 a(n) = n*(n+1)*(n+2)*(n+3)/6. 13
 0, 4, 20, 60, 140, 280, 504, 840, 1320, 1980, 2860, 4004, 5460, 7280, 9520, 12240, 15504, 19380, 23940, 29260, 35420, 42504, 50600, 59800, 70200, 81900, 95004, 109620, 125860, 143840, 163680, 185504, 209440 (list; graph; refs; listen; history; text; internal format)
 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 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 1/beta(n, 4) in A061928. Cf. A000332, A034827, A050534. Cf. A002378, A005843. Convolution of the oblong numbers with the odd numbers: A008911. Sequence in context: A196295 A196213 A196680 * A018211 A135507 A197404 Adjacent sequences:  A033485 A033486 A033487 * A033489 A033490 A033491 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified February 16 15:55 EST 2020. Contains 331961 sequences. (Running on oeis4.)