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A347041
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Stirling transform of pi (A000720).
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1
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0, 0, 1, 5, 21, 88, 389, 1852, 9525, 52632, 310141, 1936489, 12749204, 88149847, 637769490, 4812457992, 37763509549, 307453610201, 2592851608305, 22626572045811, 204197274002794, 1905132039608335, 18370391387293756, 183001650861913887, 1882207129695280320
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} pi(k)*x^k / Product_{j=1..k} (1-j*x).
E.g.f.: Sum_{k>=0} pi(k)*(exp(x)-1)^k/k!.
a(n) = Sum_{k=0..n} Stirling2(n,k)*pi(k).
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MAPLE
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b:= proc(n, m) option remember; `if`(n=0,
numtheory[pi](m), m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..27);
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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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