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 A119502 Triangle read by rows, T(n,k) = (n-k)!, for n>=0 and 0<=k<=n. 3
 1, 1, 1, 2, 1, 1, 6, 2, 1, 1, 24, 6, 2, 1, 1, 120, 24, 6, 2, 1, 1, 720, 120, 24, 6, 2, 1, 1, 5040, 720, 120, 24, 6, 2, 1, 1, 40320, 5040, 720, 120, 24, 6, 2, 1, 1, 362880, 40320, 5040, 720, 120, 24, 6, 2, 1, 1, 3628800, 362880, 40320, 5040, 720, 120, 24, 6, 2, 1, 1, 39916800 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The reciprocal of each entry in a lower triangular readout of the exponential of a matrix whose entry {j+1,j} equals one (and all other entries are zero). Note all said entries are unit fractions (all numerators are one). Denominators of unfinished fractional coefficients for polynomials A152650/A152656 = A009998/A119052. - Paul Curtz, Dec 13 2008 Multiplying the n-th diagonal by b_n with b_0 = 1 and then beheading the triangle provides a Gram matrix whose determinant is related to the reciprocal of e.g.f.s as presented in A133314. - Tom Copeland, Dec 04 2016 LINKS FORMULA T(n,k) = A025581(n,k)!. a(n) = Gamma(binomial(1 + floor((1/2) + sqrt(2*(1 + n))), 2) - n). EXAMPLE Triangle starts:    1;    1, 1;    2, 1, 1;    6, 2, 1, 1;   24, 6, 2, 1, 1; MATHEMATICA Table[Gamma[Binomial[1 + Floor[(1/2) + Sqrt[2*(1 + n)]], 2] - n], {n, 0, 77}] PROG (MAGMA) [[Factorial(n-k): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Jun 18 2015 CROSSREFS Cf. A025581. Cf. A133314. Sequence in context: A179380 A107106 A178249 * A142156 A136707 A179972 Adjacent sequences:  A119499 A119500 A119501 * A119503 A119504 A119505 KEYWORD easy,nonn,tabl AUTHOR Joseph Biberstine (jrbibers(AT)indiana.edu), May 26 2006 EXTENSIONS Name edited by Peter Luschny, Jun 17 2015 STATUS approved

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Last modified February 25 10:58 EST 2020. Contains 332230 sequences. (Running on oeis4.)