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 A039814 Matrix square of Stirling-1 Triangle A008275. 15
 1, -2, 1, 7, -6, 1, -35, 40, -12, 1, 228, -315, 130, -20, 1, -1834, 2908, -1485, 320, -30, 1, 17582, -30989, 18508, -5005, 665, -42, 1, -195866, 375611, -253400, 81088, -13650, 1232, -56, 1, 2487832, -5112570, 3805723, -1389612, 279048 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Exponential Riordan array [1/((1 + x)*(1 + log(1 + x))), log(1 + log(1 + x))]. The row sums of the unsigned array give A007840 (apart from the initial term). - Peter Bala, Jul 22 2014 Also the Bell transform of (-1)^n*A003713(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 28 2016 LINKS Vincenzo Librandi, Rows n = 1..60, flattened FORMULA E.g.f. k-th column: ((log(1+log(1+x)))^k)/k!. E.g.f.: 1/(1 + t)*( 1 + log(1 + t) )^(x-1) = 1 + (-2 + x)*t + (7 - 6*x + x^2)*t^2/2! + .... - Peter Bala, Jul 22 2014 EXAMPLE 1; -2,1; 7,-6,1; -35,40,-12,1; ... MAPLE # The function BellMatrix is defined in A264428. # Adds (1, 0, 0, 0, ..) as column 0. BellMatrix(n -> (-1)^n*add(k!*abs(Stirling1(n+1, k+1)), k=0..n), 10); # Peter Luschny, Jan 28 2016 MATHEMATICA max = 9; t = Table[StirlingS1[n, k], {n, 1, max}, {k, 1, max}]; t2 = t.t; Table[t2[[n, k]], {n, 1, max}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 01 2013 *) rows = 9; t = Table[(-1)^n*Sum[k!*Abs[StirlingS1[n+1, k+1]], {k, 0, n}], {n, 0, rows}]; T[n_, k_] := BellY[n, k, t]; Table[T[n, k], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 22 2018, after Peter Luschny *) CROSSREFS Cf. A039815-A039817. |a(n, 1)| = A003713(n) (first column). A007840. Sequence in context: A091700 A157743 A135895 * A178120 A180568 A248950 Adjacent sequences:  A039811 A039812 A039813 * A039815 A039816 A039817 KEYWORD sign,tabl,nice AUTHOR Christian G. Bower, Feb 15 1999 STATUS approved

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Last modified August 3 15:40 EDT 2020. Contains 336200 sequences. (Running on oeis4.)