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 A108786 Yet another version of the Catalan triangle A008315. 1
 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, 1, 9, 35, 75, 90, 42, 1, 10, 44, 110, 165, 132, 1, 11, 54, 154, 275, 297, 132, 1, 12, 65, 208, 429, 572, 429, 1, 13, 77, 273, 637, 1001, 1001, 429, 1, 14, 90, 350, 910, 1638, 2002 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 REFERENCES J. H. Conway and D. A. Smith, On Quaternions and Octonions, A K Peters, Ltd., Natick, MA, 2003. See p. 60. MR1957212 (2004a:17002) LINKS R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6 W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, A Pascal rhombus, Fibonacci Quarterly, 35 (1997), 318-328. EXAMPLE .......|...1 .......|.......1 .......|...1.......1 .......|.......2.......1 .......|...2.......3.......1 .......|.......5.......4.......1 .......|...5.......9.......5.......1 .......|......14......14.......6.......1 .......|..14......28......20.......7.......1 .......|......42......48......27.......8.......1 MAPLE A008315 := proc(n, k)     binomial(n, k)-binomial(n, k-1) ; end: for n from 0 to 30 do     for k from 0 to n/2 do         printf("%d, ", A008315(n, k)) ;     od: od: # R. J. Mathar, Feb 13 2008 CROSSREFS See A008315 (the main entry for this triangle) for more information. Cf. A053121, A008313, A052173. Sequence in context: A239030 A165999 A049280 * A008315 A191318 A293600 Adjacent sequences:  A108783 A108784 A108785 * A108787 A108788 A108789 KEYWORD nonn,easy,tabf AUTHOR N. J. A. Sloane, Nov 09 2006 STATUS approved

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Last modified June 20 09:12 EDT 2019. Contains 324234 sequences. (Running on oeis4.)