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A352173
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The number of Feynman graphs in phi^4 theory with n vertices, 2 external legs.
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2
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1, 2, 7, 23, 85, 340, 1517, 7489, 41276, 252410, 1706071, 12660012, 102447112, 898081422, 8477941776, 85729296020, 924345402273, 10584325318278, 128259347448244, 1639694094741643, 22053783907891362, 311294619360437722, 4601020643330758040, 71063337073204684379, 1144820435086864897289
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OFFSET
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0,2
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COMMENTS
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The generating function of this is the product of the g.f. of the connected diagrams (A352174) by the g.f. of the vacuum diagrams (A129429, including a term x^0 for the empty graph): x +2*x^2 +7*x^3 +23*x^4 ... = (x +x^2 +3*x^3 +10*x^4+ ...) * (1 +x +3*x^2 +7*x^3 +20*x^4+....). - R. J. Mathar, Mar 05 2023
a(n) is the number of multigraphs with n unlabeled nodes of degree 4 plus 2 noninterchangeable nodes of degree 1, loops allowed. - Andrew Howroyd, Mar 10 2023
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LINKS
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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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Offset corrected and a(13) and beyond from Andrew Howroyd, Mar 10 2023
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STATUS
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approved
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