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A032349
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Number of paths from (0,0) to (3n,0) that stay in first quadrant (but may touch horizontal axis), where each step is (2,1),(1,2) or (1,-1) and start with (2,1).
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11
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1, 4, 24, 172, 1360, 11444, 100520, 911068, 8457504, 80006116, 768464312, 7474561164, 73473471344, 728745517972, 7284188537672, 73301177482172, 742009157612608, 7550599410874820, 77193497566719320, 792498588659426924
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Problem 10658, American Math. Monthly, 107, 2000, 368-370.
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FORMULA
| z A^2, where A is the g. f. of A027307
a(n)=2*sum(i=0,n-1, (2*n+i-1)!/(i!*(n-i-1)!*(n+i+1)!)). [From Vladimir Kruchinin, Oct 18 2011]
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PROG
| (Maxima)
a(n):=2*sum((2*n+i-1)!/(i!*(n-i-1)!*(n+i+1)!), i, 0, n-1); [From Vladimir Kruchinin, Oct 18 2011]
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CROSSREFS
| Convolution of A027307 with itself.
Sequence in context: A027079 A188913 A052685 * A103334 A156017 A000309
Adjacent sequences: A032346 A032347 A032348 * A032350 A032351 A032352
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu)
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