

A140945


Triangle read by rows: counts seriesparallel networks by the number of series connections.


2



1, 1, 1, 1, 6, 1, 1, 25, 25, 1, 1, 90, 290, 90, 1, 1, 301, 2450, 2450, 301, 1, 1, 966, 17451, 41580, 17451, 966, 1, 1, 3025, 112035, 544971, 544971, 112035, 3025, 1, 1, 9330, 671980, 6076350, 12122502, 6076350, 671980, 9330, 1, 1, 28501, 3846700, 60738700
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OFFSET

1,5


COMMENTS

Row sums are A006351.
Second column is A000392.


LINKS

Brian Drake, Jul 24 2008, Table of n, a(n) for n = 1..153
B. Drake, An inversion theorem for labeled trees and some limits of areas under lattice paths (Example 1.5.1), A dissertation presented to the Faculty of the Graduate School of Arts and Sciences of Brandeis University.


FORMULA

E.g.f. is reversion of log(1+ax)/a+log(1+bx)/bx.
Let f(x,t) = (1+x)*(1+x*t)/(1x^2*t) and let D be the operator f(x,t)*d/dx. Then the nth row polynomial equals (D^n)(f(x,t)) evaluated at x = 0.  Peter Bala, Sep 29 2011


EXAMPLE

Triangle begins:
1;
1, 1;
1, 6, 1;
1, 25, 25, 1;
1, 90, 290, 90, 1;


MAPLE

N:=6: 1/a*log(1+a*y)+1*log(1+b*y)/by=x: solve(%, y):series(%, x, N): simplify(%, symbolic): convert(%, polynom): subs(b=1, %): R:= [seq(i!*coeff(%, x, i), i=1..N1)]: seq( seq(coeff(R[i], a, j), j=0..i1), i=1..N1);


CROSSREFS

Cf. A006351, A000392.
Sequence in context: A174045 A169660 A035348 * A141688 A166960 A155908
Adjacent sequences: A140942 A140943 A140944 * A140946 A140947 A140948


KEYWORD

easy,nonn,tabl


AUTHOR

Brian Drake, Jul 24 2008


STATUS

approved



