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 A259824 A Catalan-type triangle read by rows, generated by iteration of convolution squares. 0
 1, 1, 1, 1, 2, 2, 1, 3, 6, 4, 1, 4, 13, 16, 8, 1, 5, 24, 46, 40, 16, 1, 6, 40, 114, 140, 96, 32, 1, 7, 52, 266, 424, 392, 224, 64, 1, 8, 79, 526, 1208, 1368, 1040, 512, 128, 1, 9, 114, 1079, 3033, 4432, 4064, 2656, 1152, 256 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS The triangle is generated by an iterative procedure in which the (n+1)-st row of the following array is the convolution square of the n-th row prepended with a 1. 1, 1, 1,  1,  1,  1,   1, ...(given) 1, 2, 3,  4,  5,  6,   7, ... 1, 2, 5, 10, 18, 30,  47, ... 1, 2, 5, 14, 34, 76, 161, ... ... where the rows converge to the Catalan numbers (A000108). Example: second row of (1, 2, 3, ...) is prepended with a 1: (1, 1, 2, 3, ...), and the convolution square of that sequence is row 3 (1, 2, 5, 10, 18, ...). Next, take finite differences of terms by columns; such that the finite difference row of the n-th column becomes the n-th row of the triangle. First few rows of the triangle (as an infinite lower triangular matrix with the rest zeros) are: 1; 1, 1; 1, 2, 2; 1, 3, 6, 4; 1, 4, 13, 16, 8; 1, 5, 24, 46, 40, 16; 1, 6, 40, 114, 140, 96, 32; 1, 7, 52, 266, 424, 392, 224, 64; ... LINKS EXAMPLE Row 4 of the triangle is (1, 3, 6, 4, 0, 0, 0, ...) since the finite differences of row 4 of the array (1, 4, 10, 14, 14, ...) are (1, 3, 6, 4, 0, 0, 0, ...). CROSSREFS Cf. A000108 (row sums). Sequence in context: A082137 A091187 A318607 * A065173 A098474 A153199 Adjacent sequences:  A259821 A259822 A259823 * A259825 A259826 A259827 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Jul 05 2015 STATUS approved

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Last modified December 10 12:30 EST 2019. Contains 329895 sequences. (Running on oeis4.)