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A130410
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Alternating row sums of triangle A130191 (Stirling2)^2.
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8
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1, -1, -1, 0, 6, 32, 115, 172, -2030, -29013, -250051, -1587556, -5178877, 52922256, 1435509569, 20813187553, 230664704969, 1884809758791, 5120430335582, -216605840330716, -6440821191934686, -122368984222010397, -1842986108839510180, -21473141673616814694
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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a(n) = sum(A130191(n,m)*(-1)^m,m=0..n), n>=0.
E.g.f.: 1/exp(f(x)) with f(x):=exp(exp(x)-1)-1.
a(n) = sum(k=0..n, A000587(k)*stirling2(n,k)) = sum(k=0..n, B_k(-1)*stirling2(n,k)), where B_k(x) is k-th Bell polynomial.
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EXAMPLE
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E.g.f.: 1 - x - (1/2)*x^2 + (1/4)*x^4+(4/15)*x^5 + (23/144)*x^6 + (43/1260)*x^7 - (29/576)*x^8 - (9671/120960)*x^9 ...
G.f. = 1 - x - x^2 + 6*x^4 + 32*x^5 + 115*x^6 + 172*x^7 - 2030*x^8 - 29013*x^9 + ...
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MAPLE
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Egf:= 1/exp(exp(exp(x)-1)-1):
S:= series(Egf, x, 101):
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MATHEMATICA
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Table[Sum[BellY[n, k, -BellB[Range[n]]], {k, 0, n}], {n, 0, 23}] (* Vladimir Reshetnikov, Nov 09 2016 *)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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