A006636 - OEIS

%I M4516 #28 Mar 21 2023 17:39:17

%S 8,36,102,231,456,819,1372,2178,3312,4862,6930,9633,13104,17493,22968,

%T 29716,37944,47880,59774,73899,90552,110055,132756,159030,189280,

%U 223938,263466,308357,359136,416361,480624,552552,632808,722092,821142,930735

%N From generalized Catalan numbers.

%D H. M. Finucan, Some decompositions of generalized Catalan numbers, pp. 275-293 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H A. G. Shannon, <a href="https://nntdm.net/volume-22-2016/number-2/10-16/">Catalan triangles and Finucan's hidden folders</a>. Notes on Number Theory and Discrete Mathematics, 22(2), 10-16, (2016).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F From _Sean A. Irvine_, May 30 2017: (Start)

%F a(n) = (n + 1)*(n + 2)*(n + 4)*(n + 8)*(n + 15)/120.

%F G.f: (2 - x)^3/(x - 1)^6. (End)

%F E.g.f.: exp(x)*(960 + 3360*x + 2280*x^2 + 500*x^3 + 40*x^4 + x^5)/120. - _Stefano Spezia_, Oct 15 2022

%Y Cf. A181289.

%K nonn,easy

%O 0,1

%A _Simon Plouffe_

%E a(6) and a(8) corrected and more terms from _Sean A. Irvine_, May 30 2017