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A111670
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Array T(n,k) read by antidiagonals: the k-th column contains the first column of the k-th power of A039755.
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1
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1, 1, 1, 1, 2, 1, 1, 3, 6, 1, 1, 4, 15, 24, 1, 1, 5, 28, 105, 116, 1, 1, 6, 45, 280, 929, 648, 1, 1, 7, 66, 585, 3600, 9851, 4088, 1, 1, 8, 91, 1056, 9865, 56240, 121071, 28640, 1
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OFFSET
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1,5
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LINKS
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FORMULA
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Let A039755 (an analog of Stirling numbers of the second kind) be an infinite lower triangular matrix M; then the vector M^k * [1, 0, 0, 0, ...] (first column of the k-th power) is the k-th column of this array.
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EXAMPLE
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1 1 1 1 1 1 1 1
1 2 3 4 5 6 7 8
1 6 15 28 45 66 91 120
1 24 105 280 585 1056 1729 2640
1 116 929 3600 9865 22036 43001 76224
1 648 9851 56240 203565 565096 1318023 2717856
1 4088 121071 1029920 4953205 17148936 47920803 115146816
1 28640 1685585 21569600 138529105 600001696 2012844225 5644055040
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MAPLE
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local A, i, j ;
A := Matrix(n, n) ;
for i from 1 to n do
for j from 1 to n do
end do:
end do:
LinearAlgebra[MatrixPower](A, k) ;
%[n, 1] ;
end proc:
for d from 2 to 12 do
for n from 1 to d-1 do
end do:
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MATHEMATICA
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nmax = 10;
A[n_, k_] := Sum[(-1)^(k-j)*(2j+1)^n*Binomial[k, j], {j, 0, k}]/(2^k*k!);
A039755 = Array[A, {nmax, nmax}, {0, 0}];
T = Table[MatrixPower[A039755, n][[All, 1]], {n, 1, nmax}] // Transpose;
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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