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Search: id:A140945
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| A140945 |
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Triangle read by rows: counts series-parallel networks by the number of series connections. |
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+0
1
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| 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
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are A006351.
Second column is A000392.
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LINKS
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Brian Drake (bdrake(AT)brandeis.edu), Jul 24 2008, Table of n, a(n) for n = 1..153
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FORMULA
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E.g.f. is reversion of log(1+ax)/a+log(1+bx)/b-x.
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 6, 1;
1, 25, 25, 1;
1, 90, 290, 90, 1;
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MAPLE
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N:=6: 1/a*log(1+a*y)+1*log(1+b*y)/b-y=x: solve(%, y):series(%, x, N): simplify(%, symbolic): convert(%, polynom): subs(b=1, %): R:= [seq(i!*coeff(%, x, i), i=1..N-1)]: seq( seq(coeff(R[i], a, j), j=0..i-1), i=1..N-1);
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CROSSREFS
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Cf. A006351, A000392.
Sequence in context: A156139 A155863 A035348 this_sequence A141688 A166960 A155908
Adjacent sequences: A140942 A140943 A140944 this_sequence A140946 A140947 A140948
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Brian Drake (bdrake(AT)brandeis.edu), Jul 24 2008
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