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Search: id:A005416
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| A005416 |
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Vertex diagrams of order 2n.
(Formerly M4259)
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+0
2
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| 1, 1, 6, 50, 518, 6354, 89782, 1435330, 25625910, 505785122, 10944711398, 257834384850, 6572585595622, 180334118225650, 5300553714899094, 166206234856979810, 5538980473666776854, 195527829569946627138, 7288988096561232432070
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
P. Cvitanovic, Asymptotic estimates and gauge invariance, Nuclear Phys. B 127 (1977), 176-188.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
D. J. Broadhurst, Four-loop Dyson-Schwinger-Johnson anatomy
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FORMULA
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Let s_n=(2n)!/(2^n*n!) (A001147), S(x)=Sum_{n >= 0} s_n*x^n; sequence has g.f. A(x) satisfying 1-1/S(x)=x*A(x)*S(x).
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=sum(k=0, n+1, (2*k)!/k!/2^k*x^k, x^2*O(x^n)); polcoeff( (A-1)/(x*A^2), n))} /* Michael Somos Oct 11 2006 */
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CROSSREFS
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Cf. A049464.
Sequence in context: A090409 A039742 A125558 this_sequence A105617 A094072 A058784
Adjacent sequences: A005413 A005414 A005415 this_sequence A005417 A005418 A005419
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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