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A050169
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Triangle read by rows: T(n,k)=GCD(C(n,k),C(n,k-1)), n >= 1, 1<=k<=n.
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3
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1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 5, 10, 5, 1, 1, 3, 5, 5, 3, 1, 1, 7, 7, 35, 7, 7, 1, 1, 4, 28, 14, 14, 28, 4, 1, 1, 9, 12, 42, 126, 42, 12, 9, 1, 1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 1, 11, 55, 165, 66, 462, 66, 165, 55, 11, 1, 1, 6, 22, 55, 99, 132, 132, 99, 55, 22, 6, 1, 1, 13, 26
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Equivalently, table T(n,k)=gcd(n,k)*(n+k-1)!/(n!*k!) read by antidiagonals. - Michael Somos, Jul 19 2002
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REFERENCES
| H. Gupta, On a problem in parity, Indian J. Math., 11 (1969), 157-163. MR0260659
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FORMULA
| a(2n, n)=nth Catalan number; see A000108.
Also T(n, k)=GCD(C(n, k), C(n+1, k)).
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EXAMPLE
| 1; 1,1; 1,3,1; 1,2,2,1; 1,5,10,5,1; 1,3,5,5,3,1; ...
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PROG
| (PARI) T(n, k)=if(n<1|k<1, 0, gcd(n, k)*(n+k-1)!/n!/k!)
(PARI) T(n, k)=if(k<1|k>n, 0, gcd(n+1, k)*binomial(n, k-1)/k) - Michael Somos Mar 03 2004
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CROSSREFS
| Cf. A002784, A178252.
Sequence in context: A126209 A176346 A073166 * A143214 A175636 A204253
Adjacent sequences: A050166 A050167 A050168 * A050170 A050171 A050172
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Offset set to 1 - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 21 2010
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