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A359985
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Triangle read by rows: T(n,k) is the number of quasi series-parallel matroids on [n] with rank k, 0 <= k <= n.
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4
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1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 35, 15, 1, 1, 31, 155, 155, 31, 1, 1, 63, 651, 1365, 651, 63, 1, 1, 127, 2667, 10941, 10941, 2667, 127, 1, 1, 255, 10795, 82215, 156597, 82215, 10795, 255, 1, 1, 511, 43435, 589135, 1988007, 1988007, 589135, 43435, 511, 1
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OFFSET
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0,5
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COMMENTS
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A quasi series-parallel matroid is a collection of series-parallel matroids. See the Ferroni/Larson reference for a precise definition.
The first six rows of this triangle are the same as A022166.
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LINKS
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 3, 1;
1, 7, 7, 1;
1, 15, 35, 15, 1;
1, 31, 155, 155, 31, 1;
1, 63, 651, 1365, 651, 63, 1;
1, 127, 2667, 10941, 10941, 2667, 127, 1;
...
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PROG
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(PARI) \\ Proposition 2.3, 2.8 in Ferroni/Larson, compare A140945.
T(n) = {[Vecrev(p) | p<-Vec(serlaplace(exp(x*(y+1) + y*intformal( serreverse(log(1 + x*y + O(x^n))/y + log(1 + x + O(x^n)) - x)))))]}
{ my(A=T(8)); for(i=1, #A, print(A[i])) }
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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