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A226261
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Denominators of mass formula for connected vacuum graphs on 2n nodes for a phi^3 field theory.
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3
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1, 24, 16, 1152, 128, 3072, 96, 688128, 4096, 7077888, 4096, 46137344, 24576, 436207616, 114688, 6442450944, 2097152, 876173328384, 9437184, 15668040695808, 8388608, 138538465099776, 1441792, 4855443348258816, 201326592, 1688849860263936, 872415232
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OFFSET
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0,2
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LINKS
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FORMULA
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Let V(n) = (3*n - 1)!!/(3!^n*n!), and c(n) = V(2*n) - (1/n)*Sum_{j=0..n-1} j*c(j)*V(2*(n-j)), c(0) = 1. Then a(n) = denominator of c(n). - Franck Maminirina Ramaharo, Feb 04 2019
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EXAMPLE
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1, 5/24, 5/16, 1105/1152, 565/128, 82825/3072, 19675/96, 1282031525/688128, 80727925/4096, ...
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PROG
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(Maxima)
c_list : [1]$
V(n) := if n = 0 then 1 else (3*n - 1)!!/(3!^n*n!)$
c(n) := V(2*n) - 1/n*sum(j*c_list[j + 1]*V(2*(n - j)), j , 0 , n - 1)$
for i:1 thru 50 do c_list : append(c_list, [c(i)])$
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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