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Search: id:A059366
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| A059366 |
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Triangle T(m,s), m >= 0, 0<=s<=m, arising in computation of certain integrals. |
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2
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| 1, 1, 1, 3, 2, 3, 15, 9, 9, 15, 105, 60, 54, 60, 105, 945, 525, 450, 450, 525, 945, 10395, 5670, 4725, 4500, 4725, 5670, 10395, 135135, 72765, 59535, 55125, 55125, 59535, 72765, 135135, 2027025, 1081080, 873180, 793800, 771750, 793800, 873180
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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T(n,s)=A000984(s)*A000984(n-s)*A000142(n)/A000079(n); T(n,s)=T(n,n-s); Sum(T(n,s):0<=s<=n)=A000165(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 10 2004
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 167, a(m,s).
Konrad Jacobs, Selecta Mathematica I (Springer 1969), Das kombinatorische arcsin-Gesetz, Lemma 3.3.
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FORMULA
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T(m+2, s) = (2*m+3)*(T(m+1, s-1)+T(m+1, s)) - 4*(m+1)^2*T(m, s-1). T(m, s) = Sum_{k=0..s} binomial(s, k)*binomial(2*m-2*k, s)*binomial(2*m-2*k-s, m-k).
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EXAMPLE
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1; 1,1; 3,2,3; 15,9,9,15; ...
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CROSSREFS
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Main diagonal gives A001757.
Sequence in context: A078017 A057053 A081850 this_sequence A092950 A059239 A123170
Adjacent sequences: A059363 A059364 A059365 this_sequence A059367 A059368 A059369
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KEYWORD
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tabl,nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 28 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Feb 08 2001
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