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A039814
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Matrix square of Stirling-1 Triangle A008275.
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15
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Rows n = 1..60, flattened
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FORMULA
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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
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EXAMPLE
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1; -2,1; 7,-6,1; -35,40,-12,1; ...
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MAPLE
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# 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
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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sign,tabl,nice
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AUTHOR
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Christian G. Bower, Feb 15 1999
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STATUS
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approved
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