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 A048966 A convolution triangle of numbers obtained from A025748. 6
 1, 3, 1, 15, 6, 1, 90, 39, 9, 1, 594, 270, 72, 12, 1, 4158, 1953, 567, 114, 15, 1, 30294, 14580, 4482, 1008, 165, 18, 1, 227205, 111456, 35721, 8667, 1620, 225, 21, 1, 1741905, 867834, 287199, 73656, 15075, 2430, 294, 24, 1, 13586859, 6857136, 2328183, 623106, 136323, 24354, 3465, 372, 27, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A generalization of the Catalan triangle A033184. LINKS Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4. FORMULA a(n, m) = 3*(3*(n-1)-m)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n= m >= 1 := a[n, m] = 3*(3*(n-1) - m)*a[n-1, m]/n + m*a[n-1, m-1]/n; a[n_, m_] /; n < m := 0; a[n_, 0] = 0; a[1, 1] = 1; Table[a[n, m], {n, 1, 10}, {m, 1, n}] // Flatten (* Jean-François Alcover, Apr 26 2011, after given formula *) PROG (Haskell) a048966 n k = a048966_tabl !! (n-1) !! (k-1) a048966_row n = a048966_tabl !! (n-1) a048966_tabl = [1] : f 2 [1] where    f x xs = ys : f (x + 1) ys where      ys = map (flip div x) \$ zipWith (+)           (map (* 3) \$ zipWith (*) (map (3 * (x - 1) -) [1..]) (xs ++ [0]))           (zipWith (*) [1..] ([0] ++ xs)) -- Reinhard Zumkeller, Feb 19 2014 CROSSREFS Cf. A034000, A049213, A049223, A049224. a(n, 1)= A025748(n), a(n, 1)= 3^(n-1)*2*A034000(n-1)/n!, n >= 2. Row sums = A025756. Sequence in context: A144815 A065250 A092589 * A297704 A104990 A089463 Adjacent sequences:  A048963 A048964 A048965 * A048967 A048968 A048969 KEYWORD easy,nonn,tabl,nice AUTHOR STATUS approved

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Last modified April 23 05:42 EDT 2021. Contains 343199 sequences. (Running on oeis4.)