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A120058
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Coefficients for obtaining A120057 from Bell numbers.
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3
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1, 2, -1, 3, -4, 2, 4, -9, 10, -4, 5, -16, 28, -24, 8, 6, -25, 60, -80, 56, -16, 7, -36, 110, -200, 216, -128, 32, 8, -49, 182, -420, 616, -560, 288, -64, 9, -64, 280, -784, 1456, -1792, 1408, -640, 128, 10, -81, 408, -1344, 3024, -4704, 4992, -3456, 1408, -256
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Appears to be essentially the same as A056863, but (as of Jun 06 2006) that sequence definition is unclear and there are discrepencies in the signs.
Alternating column sums appear to be 3^n.
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LINKS
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Table of n, a(n) for n=1..55.
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FORMULA
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A120057(n,k) = sum_{i=1,k} T(n,i)*B(n-i+1).
T(n,k) = Sum_j A120095(n,j) * S1(j,n-k+1), where S1 is the Stirling numbers of the first kind (A008275).
Unsigned version, as an infinite lower triangular matrix, equals A007318 * A134315. - Gary W. Adamson, Oct 19 2007
T(n,k) = 2*T(n-1,k) - 2*T(n-1,k-1) + 2*T(n-2,k-1) - T(n-2,k). - Philippe Deléham, Feb 27 2012
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EXAMPLE
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Table starts:
1
2,-1
3,-4,2
4,-9,10,-4
5,-16,28,-24,8
6,-25,60,-80,56,-16
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MATHEMATICA
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T[n_, 1] := n; T[n_, n_] := (-1)^(n+1)*2^(n-2); T[n_, k_] /; 2 <= k <= n-1 := T[n, k] = 2*T[n-1, k] - 2*T[n-1, k-1] + 2*T[n-2, k-1] - T[n-2, k]; T[_, _] = 0; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Apr 08 2016, after Philippe Deléham *)
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CROSSREFS
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Cf A120057, A000110, A056863.
Cf. A008275, A120095.
Cf. A134315.
Sequence in context: A209151 A125100 A128544 * A208532 A245334 A102756
Adjacent sequences: A120055 A120056 A120057 * A120059 A120060 A120061
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KEYWORD
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sign,tabl
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AUTHOR
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Franklin T. Adams-Watters, Jun 06 2006, Jun 07 2006
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STATUS
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approved
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