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A169715
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The function W_6(2n) (see Borwein et al. reference for definition).
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8
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1, 6, 66, 996, 18306, 384156, 8848236, 218040696, 5651108226, 152254667436, 4229523740916, 120430899525096, 3499628148747756, 103446306284890536, 3102500089343886696, 94219208840385966096, 2892652835496484004226, 89662253086458906345036
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OFFSET
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0,2
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COMMENTS
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a(n)/6^(2n) is the probability that two throws of n 6-sided dice will give the same result - Henry Bottomley, Aug 30 2016
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LINKS
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FORMULA
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Sum_{n>=0} a(n)*x^n/n!^2 = (Sum_{n>=0} x^n/n!^2)^6 = BesselI(0, 2*sqrt(x))^6. - Peter Bala, Mar 05 2013
Recurrence: n^5*a(n) = 2*(2*n-1)*(14*n^4 - 28*n^3 + 28*n^2 - 14*n + 3)*a(n-1) - 4*(n-1)^3*(196*n^2 - 392*n + 255)*a(n-2) + 1152*(n-2)^2*(n-1)^2*(2*n-3)*a(n-3). - Vaclav Kotesovec, Mar 09 2014
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MAPLE
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W := proc(n, s)
local a, ai ;
if s = 0 then
return 1;
end if;
a := 0 ;
for ai in combinat[partition](s/2) do
if nops(ai) <= n then
af := [op(ai), seq(0, i=1+nops(ai)..n)] ;
a := a+combinat[numbperm](af)*(combinat[multinomial](s/2, op(ai)))^2 ;
end if ;
end do;
a ;
end proc:
W(6, 2*n) ;
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MATHEMATICA
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max = 17; Total /@ MatrixPower[Table[Binomial[n, k]^2, {n, 0, max}, {k, 0, max}], 5] (* Jean-François Alcover, Mar 24 2015, after Peter Bala *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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