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A098384
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Triangle read by rows of coefficients used to generate diagonals of ordered factorizations as displayed in A098348.
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2
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1, 3, 2, 13, 18, 8, 75, 158, 144, 48, 541, 1530, 2120, 1440, 384, 4683, 16622, 30960, 31920, 17280, 3840
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OFFSET
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0,2
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COMMENTS
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Note that the table includes the well-known sequence (A000165) discussed by Gordon on pages 636-645 of AMM 106 (1999).
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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From Peter Bala, Apr 20 2012: (Start)
The following formulas are all conjectural:
T(n,k) = 2^k*sum {i = k+1..n+1} binomial(i,k+1)*(i-1)!*Stirling2(n+1,i) = 1/(k+1)*A194649(n+1,k).
Recurrence equation:
T(n,k) = 2*k*T(n-1,k-1) + 3*(k+1)*T(n-1,k) + (k+2)*T(n-1,k+1).
E.g.f.: exp(x)/((2-exp(x))*(2*t+2-(2*t+1)*exp(x))) = 1 + (3+2*t)*x + (13+18*t+8*t^2)*x^2/2! + ....
Column n generating function: 2^n*exp(x)*(1-exp(x))^n/(exp(x)-2)^(n+2) for n >= 0.
(End)
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EXAMPLE
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The table begins:
1
3 2
13 18 8
75 158 144 48
541 1530 2120 1440 384
The binomial transform of (13,18,8) yields 13,31,57,91,...
The binomial transform of 13,31,57,91,... yields 13,44,132,368,... A098385
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CROSSREFS
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Cf. A000165, A052876, A098348, A098385. A194649.
Sequence in context: A095131 A060149 A059374 * A064536 A163355 A214885
Adjacent sequences: A098381 A098382 A098383 * A098385 A098386 A098387
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KEYWORD
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nonn,tabl
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AUTHOR
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Alford Arnold, Sep 06 2004
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STATUS
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approved
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