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 A137854 Triangle generated from an array: A008277 * A008277(transform). 1
 1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 11, 8, 1, 1, 16, 28, 28, 16, 1, 1, 32, 71, 87, 71, 32, 1, 1, 64, 184, 266, 266, 184, 64, 1, 1, 128, 491, 823, 952, 823, 491, 128, 1, 1, 256, 1348, 2598, 3381, 381, 2598, 1348, 2561 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums = A000995 such that row 1 = A000995(3) = 1. This array is the product of the lower triangular Stirling matrix and its transpose, which explains why the array is symmetric. - David Callan, Dec 02 2011 In the triangle, T(n,k) is the number of permutations of [n+1] that avoid both dashed patterns 1-23 and 3-12, start with an ascent, and have first entry k. For example, T(4,2)=4 counts 23154, 24153, 24315, 25431. - David Callan, Dec 02 2011 LINKS Table of n, a(n) for n=1..54. FORMULA Triangle read by rows = antidiagonals of an array formed by A008277 * A008277(transform), where A008277 = the Stirling number of the second kind triangle. EXAMPLE First few rows of the array: 1, 1, 1, 1, 1, 1, ... 1, 2, 4, 8, 16, 32, ... 1, 4, 11, 28, 71, 184, ... 1, 8, 28, 87, 266, 823, ... 1, 16, 71, 266, 952, 3381, ... ... First few rows of the triangle: 1; 1, 1; 1, 2, 1; 1, 4, 4, 1; 1, 8, 11, 8, 1; 1, 16, 28, 28, 16, 1; 1, 32, 71, 87, 71, 32, 1; 1, 64, 184, 266, 266, 184, 64, 1; 1, 128, 491, 823, 952, 823, 491, 128, 1; ... CROSSREFS Cf. A000995, A008277. Sequence in context: A202979 A306326 A156006 * A062715 A100631 A154867 Adjacent sequences: A137851 A137852 A137853 * A137855 A137856 A137857 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Feb 15 2008 STATUS approved

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Last modified June 17 13:47 EDT 2024. Contains 373445 sequences. (Running on oeis4.)