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A071949
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Triangle read by rows of numbers of paths in a lattice satisfying certain conditions.
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0
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1, 1, 2, 1, 4, 10, 1, 6, 24, 66, 1, 8, 42, 172, 498, 1, 10, 64, 326, 1360, 4066, 1, 12, 90, 536, 2706, 11444, 34970, 1, 14, 120, 810, 4672, 23526, 100520, 312066, 1, 16, 154, 1156, 7410, 42024, 211546, 911068, 2862562, 1, 18, 192, 1582, 11088, 69002, 387456
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, On some alternative characterizations of Riordan arrays, Canad J. Math., 49 (1997), 301-320.
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FORMULA
| T(n, k)= (n-k+1)sum(2^(j+1)*binomial(k, j+1)*binomial(n+k, j), j=0..k-1)/k for 0<k<=n; T(n, 0)=1; T(n, k)=0 for k>n.
T(n,0) = 1, T(n,n) = T(n,n-1) + T(n+1,n-1), otherwise T(n,k) = T(n,k-1) + T(n+1,k-1) + T(n-1,k). [From Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Oct 09 2008]
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EXAMPLE
| 1; 1,2; 1,4,10; 1,6,24,66; 1,8,42,172,498;
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MAPLE
| T := proc(n, k) if k>0 and k<=n then (n-k+1)*sum(2^(j+1)*binomial(k, j+1)*binomial(n+k, j), j=0..k-1)/k elif k=0 then 1 else 0 fi end: seq(seq(T(n, k), k=0..n), n=0..10);
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CROSSREFS
| T(n, n)=A027307(n).
Sequence in context: A117338 A137634 A100229 * A156919 A179077 A038195
Adjacent sequences: A071946 A071947 A071948 * A071950 A071951 A071952
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 15 2002
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EXTENSIONS
| Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 04 2004
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