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Search: id:A048594
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| A048594 |
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Triangle a(n,k) = k! * Stirling1(n,k), 1<=k<=n. |
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+0
12
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| 1, -1, 2, 2, -6, 6, -6, 22, -36, 24, 24, -100, 210, -240, 120, -120, 548, -1350, 2040, -1800, 720, 720, -3528, 9744, -17640, 21000, -15120, 5040, -5040, 26136, -78792, 162456, -235200, 231840, -141120, 40320, 40320, -219168, 708744, -1614816, 2693880, -3265920, 2751840
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums (unsigned) give A007840(n), n>=1; (signed): A006252(n), n>=1.
Apart from signs, coefficients in expansion of n-th derivative of 1/ln(x).
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FORMULA
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a(n, k)= k*a(n-1, k-1)-(n-1)*a(n-1, k) if n>=k>=1, a(n, 0) := 0 and a(1, 1)=1, else 0.
E.g.f. k-th column: ln(1+x)^k, k>=1.
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EXAMPLE
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1; -1,2; 2,-6,6; -6,22,-36,24; 24,-100,210,-240,120; ...
2nd derivative of 1/ln(x) is -2/x^3*ln(x)^2-6/x^3*ln(x)^3-6/x^3*ln(x)^4.
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MAPLE
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with(combinat): A048594 := (n, k)->k!*stirling1(n, k);
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MATHEMATICA
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Table[ D[ 1/Log[ z ], {z, n} ], {n, 10} ]
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PROGRAM
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(PARI) {T(n, k)= if(k<1| k>n, 0, stirling(n, k)* k!)} /* Michael Somos Apr 11 2007 */
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CROSSREFS
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Cf. A008275, A019538, A075181.
Adjacent sequences: A048591 A048592 A048593 this_sequence A048595 A048596 A048597
Sequence in context: A084700 A122766 A033742 this_sequence A130493 A010762 A055993
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KEYWORD
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sign,tabl,easy,nice
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AUTHOR
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Oleg Marichev (oleg(AT)wolfram.com)
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