

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
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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

Table of n, a(n) for n=0..70.
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), 318328.


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, k1) ;
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



