

A098384


Triangle read by rows of coefficients used to generate diagonals of ordered factorizations as displayed in A098348.


2



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

0,2


COMMENTS

Note that the table includes the wellknown sequence (A000165) discussed by Gordon on pages 636645 of AMM 106 (1999).


LINKS

Table of n, a(n) for n=0..20.


FORMULA

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)*(i1)!*Stirling2(n+1,i) = 1/(k+1)*A194649(n+1,k).
Recurrence equation:
T(n,k) = 2*k*T(n1,k1) + 3*(k+1)*T(n1,k) + (k+2)*T(n1,k+1).
E.g.f.: exp(x)/((2exp(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)*(1exp(x))^n/(exp(x)2)^(n+2) for n >= 0.
(End)


EXAMPLE

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


CROSSREFS

Cf. A000165, A052876, A098348, A098385. A194649.
Sequence in context: A095131 A060149 A059374 * A243253 A064536 A231183
Adjacent sequences: A098381 A098382 A098383 * A098385 A098386 A098387


KEYWORD

nonn,tabl


AUTHOR

Alford Arnold, Sep 06 2004


STATUS

approved



