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 A140356 Triangle T(n,m) read by rows: m! if m <= floor(n/2), and (n-m)! otherwise. 2
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 6, 2, 1, 1, 1, 1, 2, 6, 6, 2, 1, 1, 1, 1, 2, 6, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 120, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 120, 120, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 120, 720, 120, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Row sums: 1, 2, 3, 4, 6, 8, 14, 20, 44, 68, 188,... which is 2*A003422((n+1)/2) if n is odd, and A003422(n/2)+A003422(1+n/2) if n is even. LINKS Table of n, a(n) for n=0..95. FORMULA T(n,m) = A000142(m) if m<=[n/2], = A000142(n-m) if m>[n/2], 0<=m<=n. Conjecture: limit_{n->infinity} sum_{m=0..n} ( 1/binomial(n,m) - T(n,m) ) = 0. T(n,m) = T(n,n-m). EXAMPLE 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 6, 2, 1, 1, 1, 1, 2, 6, 6, 2, 1, 1, 1, 1, 2, 6, 24, 6, 2, 1,1, 1, 1, 2, 6, 24, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 120, 24, 6, 2, 1, 1 MATHEMATICA g[n_, m_] := If[m <= Floor[n/2], m!, (n - m)! ]; w = Table[Table[g[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[w] Table[Apply[Plus, Table[g[n, m], {m, 0, n}]], {n, 0, 10}] CROSSREFS Sequence in context: A139147 A055801 A155050 * A119963 A057790 A350889 Adjacent sequences: A140353 A140354 A140355 * A140357 A140358 A140359 KEYWORD nonn,easy,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, May 30 2008 EXTENSIONS Non-Ascii characters corrected, offset set to 0, reported Mma experiments removed - The Assoc. Editors of the OEIS, Oct 31 2009 STATUS approved

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Last modified September 12 02:35 EDT 2024. Contains 375842 sequences. (Running on oeis4.)