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A098620
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Consider the family of multigraphs enriched by the species of set partitions. Sequence gives number of those multigraphs with n labeled edges.
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13
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1, 1, 4, 26, 257, 3586, 66207, 1540693, 43659615, 1469677309, 57681784820, 2601121752854, 133170904684965, 7664254746784243, 491679121677763607, 34905596059311761907, 2725010800987216480527, 232643959843709167832482, 21613761720729431904201734
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OFFSET
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0,3
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REFERENCES
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G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
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LINKS
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FORMULA
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PROG
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(PARI) \\ here R(n) is A000110 as e.g.f.
egf1(n)={my(bell=serlaplace(exp(exp(x + O(x^(2*n+1)))-1))); sum(i=0, n, sum(k=0, i, (-1)^k*binomial(i, k)*polcoef(bell, 2*i-k))*x^i/i!) + O(x*x^n)}
EnrichedGnSeq(R)={my(n=serprec(R, x)-1, B=exp(x/2 + O(x*x^n))*subst(egf1(n), x, log(1+x + O(x*x^n))/2)); Vec(serlaplace(subst(B, x, R-polcoef(R, 0))))}
R(n)={exp(exp(x + O(x*x^n))-1)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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