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A122486
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a(n) = Sum_{k=0..n} |Stirling1(n,k)|*Bell(k)^2.
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0
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1, 1, 5, 39, 425, 6053, 107735, 2321469, 59152987, 1750362419, 59286010621, 2271617296347, 97502863649141, 4649359584613201, 244550369307356039, 14101227268075911837, 886551391533830227267, 60482082002935189216499
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OFFSET
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0,3
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COMMENTS
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Row sums of the absolute values of the triangle of Stirling1(n,k)*Bell(k)^2:
1;
0, 1;
0, -1, 4;
0, 2, -12, 25;
0, -6, 44, -150, 225;
0, 24, -200, 875, -2250, 2704;
0, -120, 1096, -5625, 19125, -40560, 41209;
0, 720, -7056, 40600, -165375, 473200, -865389, 769129;
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LINKS
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FORMULA
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a(n) = exp(-2)*Sum_{r,s>=0} [r*s]^n/(r!*s!), where [m]^n = m*(m+1)*...*(m+n-1) is the rising factorial.
E.g.f.: Sum_{n>=0} exp( 1/(1-x)^n - 2 ) / n!. - Paul D. Hanna, Jul 25 2018
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MAPLE
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with(combinat): seq(sum(abs(stirling1(n, k))*bell(k)^2, k=0..n), n=0..19); # Emeric Deutsch, Oct 08 2006
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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