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A156792
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Triangle read by rows, T(n,k) = (A156791(n-k+1) * (A006973 * 0^(n-k))).
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3
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1, 1, 1, 6, 1, 2, 7, 6, 2, 9, 78, 7, 12, 9, 24, 420, 78, 14, 54, 24, 130, 6872, 420, 156, 63, 144, 130, 720, 17253, 6872, 840, 702, 168, 780, 720, 8505, 326552, 17253, 13744, 3780, 1872, 910, 4320, 8505, 35840
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OFFSET
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0,4
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COMMENTS
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As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.
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LINKS
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FORMULA
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Triangle read by rows, T(n,k) = M*Q =(A156791(n-k+1) * (A006973 * 0^(n-k)))
M = an infinite lower triangular matrix with A156791: (1, 1, 6, 7, 78, ...) in every column.
Q = an infinite lower triangular matrix with A006973 prefaced with a 1 as the main diagonal: (1, 1, 2, 9, 24, 130, 720, 8505, ...) and the rest zeros.
Sum_{k=0..n} T(n, k) = A006973(n+1).
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EXAMPLE
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First few rows of the triangle:
1,
1, 1;
6, 1, 2;
7, 6, 2, 9;
78, 7, 12, 9, 24;
420, 78, 14 54, 24, 130;
6872, 420, 156, 63, 144, 130, 720;
17253, 6872, 840, 702, 168, 780, 720, 8505;
326552, 17253, 13744, 3780, 1872, 910, 4320, 8505, 35840;
...
Example: Row 4 = (7, 6, 2, 9) = termwise products of (7, 6, 1, 1) and (1, 1, 2, 9).
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MATHEMATICA
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A006973[n_]:= A006973[n]= If[n<4, Max[n-1, 0], (n-1)!*(1 + Sum[k*(-A006973[k]/k!)^(n/k), {k, Most[Divisors[n]]}])];
S[n_, x_]:= Sum[A006973[j]*x^j, {j, 0, n+2}];
A156791:= With[{p=100}, CoefficientList[Series[S[p, x]/(x + S[p, x]), {x, 0, p}], x]]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Typo in last line of triangle corrected by Olivier Gérard, Aug 11 2016
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STATUS
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approved
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