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Search: id:A124644
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| 1, 1, 1, 2, 2, 1, 5, 6, 3, 1, 14, 20, 12, 4, 1, 42, 70, 50, 20, 5, 1, 132, 252, 210, 100, 30, 6, 1, 429, 924, 882, 490, 175, 42, 7, 1, 1430, 3432, 3696, 2352, 980, 280, 56, 8, 1, 4862, 12870, 15444, 11088, 5292, 1764, 420, 72, 9, 1, 16796, 48620, 64350, 51480, 27720
(list; table; graph; listen)
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OFFSET
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0,4
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FORMULA
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T(n,k)=[x^(n-k)]F(-n,n-k+1;1;-1-x); [From Paul Barry (pbarry(AT)wit.ie), Sep 05 2008]
G.f.: 1/(1-xy-x/(1-x/(1-xy-x/(1-x/(1-xy-x/(1-x.... (continued fraction); [From Paul Barry (pbarry(AT)wit.ie), Jan 06 2009]
G.f.: 1/(1-x-xy-x^2/(1-2x-xy-x^2/(1-2x-xy-x^2/(1-.... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Jan 28 2009]
T(n,k)=sum{i=0..n, C(n,i)*(-1)^(n-i)*sum{j=0..i, C(j,k)*C(i,j)*A000108(i-j)}}. [From Paul Barry (pbarry(AT)wit.ie), Aug 03 2009]
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EXAMPLE
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Contribution from Paul Barry (pbarry(AT)wit.ie), Jan 28 2009: (Start)
Triangle begins
1,
1, 1,
2, 2, 1,
5, 6, 3, 1,
14, 20, 12, 4, 1,
42, 70, 50, 20, 5, 1 (End)
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MAPLE
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m:=n->binomial(2*n, n)/(n+1): T:=proc(n, k) if k<=n then binomial(n, k)*m(n-k) else 0 fi end: for n from 0 to 10 do seq(T(n, k), k=0..n) od;
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CROSSREFS
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Cf. A098474.
Sequence in context: A010094 A019710 A118806 this_sequence A056857 A129100 A162382
Adjacent sequences: A124641 A124642 A124643 this_sequence A124645 A124646 A124647
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KEYWORD
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nonn,tabl
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AUTHOR
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Farkas Janos Smile (smile_farkasjanos(AT)yahoo.com.au), Dec 21 2006
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