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 A091063 Triangle, read by rows, such that the initial terms of the binomial transform of the n-th row forms the n-th row of triangle A059438 transposed (permutations of [1..n] with k components). 2
 1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 7, 0, 1, 4, 9, 18, 34, 0, 1, 5, 14, 34, 86, 206, 0, 1, 6, 20, 56, 162, 508, 1476, 0, 1, 7, 27, 85, 269, 939, 3549, 12123, 0, 1, 8, 35, 122, 415, 1540, 6413, 28498, 111866, 0, 1, 9, 44, 168, 609, 2361, 10314, 50382, 257922, 1143554, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS The main diagonal equals A075834 shift 1 place left; subsequent diagonals of this triangle are self-convolutions of the main diagonal. A075834 has the property that the n-th term of the n-th self-convolution of A075834 equals n!. The first (n+1) terms of the binomial transform of the n-th row forms the n-th row of triangle A059438 transposed, which has row sums equal to the factorials. A059438 is also formed from the self-convolutions of its main diagonal (A003319). LINKS EXAMPLE Rows begin: {1}, {1,0}, {1,1,0}, {1,2,2,0}, {1,3,5,7,0}, {1,4,9,18,34,0}, {1,5,14,34,86,206,0}, {1,6,20,56,162,508,1476,0}, {1,7,27,85,269,939,3549,12123,0},... Initial terms of the binomial transform of each row forms A059438: {1}, {1,1}, {1,2,3}, {1,3,7,13}, {1,4,12,32,71}, {1,5,18,58,177,461}, {1,6,25,92,327,1142,3447}, {1,7,33,135,531,2109,8411,29093}, {1,8,42,188,800,3440,15366,69692,273343},... which has row sums equal to the factorials. CROSSREFS Cf. A075834, A059438, A003319. Sequence in context: A130020 A292870 A306704 * A246935 A342120 A198793 Adjacent sequences:  A091060 A091061 A091062 * A091064 A091065 A091066 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Dec 17 2003 STATUS approved

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Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)