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A226259
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Denominators of mass formula for connected vacuum graphs on n nodes for a phi^4 field theory.
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3
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1, 8, 12, 96, 72, 960, 324, 96768, 1296, 82944, 1620, 3649536, 17496, 77635584, 6804, 159252480, 23328, 9746251776, 708588, 392143306752, 2361960, 866843099136, 7794468, 22785590034432, 25509168, 445805022412800, 82904796, 213986410758144, 29760696
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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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EXAMPLE
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1, 1/8, 1/12, 11/96, 17/72, 619/960, 709/324, ...
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PROG
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(Maxima)
c_list : [1]$
V(n) := if n = 0 then 1 else (4*n - 1)!!/(4!^n*n!)$
c(n) := V(n) - 1/n*sum(j*c_list[j + 1]*V(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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