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A108786 Yet another version of the Catalan triangle A008315.

%I A108786 #15 Jan 05 2025 19:51:38
%S A108786 1,1,1,1,1,2,1,3,2,1,4,5,1,5,9,5,1,6,14,14,1,7,20,28,14,1,8,27,48,42,
%T A108786 1,9,35,75,90,42,1,10,44,110,165,132,1,11,54,154,275,297,132,1,12,65,
%U A108786 208,429,572,429,1,13,77,273,637,1001,1001,429,1,14,90,350,910,1638,2002
%N A108786 Yet another version of the Catalan triangle A008315.
%D A108786 J. H. Conway and D. A. Smith, On Quaternions and Octonions, A K Peters, Ltd., Natick, MA, 2003. See p. 60. MR1957212 (2004a:17002)
%H A108786 R. K. Guy, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/GUY/catwalks.html">Catwalks, sandsteps and Pascal pyramids</a>, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6
%H A108786 W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/35-4/klostermeyer.pdf">A Pascal rhombus</a>, Fibonacci Quarterly, 35 (1997), 318-328.
%e A108786 .......|...1
%e A108786 .......|.......1
%e A108786 .......|...1.......1
%e A108786 .......|.......2.......1
%e A108786 .......|...2.......3.......1
%e A108786 .......|.......5.......4.......1
%e A108786 .......|...5.......9.......5.......1
%e A108786 .......|......14......14.......6.......1
%e A108786 .......|..14......28......20.......7.......1
%e A108786 .......|......42......48......27.......8.......1
%p A108786 A008315 := proc(n,k)
%p A108786     binomial(n,k)-binomial(n,k-1) ;
%p A108786 end:
%p A108786 for n from 0 to 30 do
%p A108786     for k from 0 to n/2 do
%p A108786         printf("%d, ",A008315(n,k)) ;
%p A108786     od:
%p A108786 od: # _R. J. Mathar_, Feb 13 2008
%Y A108786 See A008315 (the main entry for this triangle) for more information.
%Y A108786 Cf. A053121, A008313, A052173.
%K A108786 nonn,easy,tabf
%O A108786 0,6
%A A108786 _N. J. A. Sloane_, Nov 09 2006