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 A202212 Triangle read by rows: T(n,k) (1 <= k <= n-1, n >= 2) = d(2*(n-k)-1)*(d(2*n-2)/d(2*(n-k)-2) - d(2*n-3)/d(2*(n-k)-3)), where d = A006882 is the double factorial function. 2
 1, 3, 5, 15, 27, 33, 105, 195, 261, 279, 945, 1785, 2475, 2925, 2895, 10395, 19845, 28035, 34425, 37935, 35685, 135135, 259875, 371385, 465255, 533925, 562275, 509985, 2027025, 3918915, 5644485, 7158375, 8390025, 9218475, 9401805, 8294895, 34459425, 66891825, 96891795, 123898005, 147093975, 165209625, 176067675, 175313565, 151335135, 654729075, 1274998725, 1854727875, 2385808425, 2857013775, 3252014325, 3545408475, 3693650625, 3609649575, 3061162125 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 REFERENCES N. Ochiumi, On the total sum of number of nodes covering a given number of leaves in an unordered binary tree; http://www.math.tohoku.ac.jp/~sa9d05/cos2011/abst/ochiumi.pdf. LINKS EXAMPLE Triangle begins 1, 3, 5, 15, 27, 33, 105, 195, 261, 279, 945, 1785, 2475, 2925, 2895, 10395, 19845, 28035, 34425, 37935, 35685, 135135, 259875, 371385, 465255, 533925, 562275, 509985, ... MAPLE d:=doublefactorial; a:=(n, k)-> d(2*(n-k)-1)*(d(2*n-2)/d(2*(n-k)-2) - d(2*n-3)/d(2*(n-k)-3)); f:=n->[seq(a(n, k), k=1..n-1)]; for n from 1 to 10 do lprint(f(n)); od: CROSSREFS Edges of triangle are A006882 and A129890. Sequence in context: A163114 A111386 A146582 * A053351 A146244 A146457 Adjacent sequences:  A202209 A202210 A202211 * A202213 A202214 A202215 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Dec 14 2011 STATUS approved

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Last modified June 19 09:12 EDT 2013. Contains 226401 sequences.