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A014619
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Exponential generating function is -f(x) * int(exp(exp(-t)-1),t,0,x) where f(x) = exp(1-x-exp(-x)) is an exponential generating function for A014182.
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10
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-1, 1, 1, -5, 5, 21, -105, 141, 777, -5513, 13209, 39821, -527525, 2257425, -41511, -70561285, 531862173, -1559180499, -8858267353, 147780183829, -936560917615, 1352130196615, 38710924110081, -487251979381019, 2846575686392251, 872653153712201
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OFFSET
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1,4
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LINKS
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FORMULA
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E.g.f. A(x) = y satisfies y'' + y'(2-exp(-x)) + y = 0. - Michael Somos, Mar 11 2004
The sequence b(n) = (-1)^n*a(n) satisfies the recurrence: b(n) = -Sum_{i = 1..n} b(i-1)*C(n, i) ], b(0) = -1. - Ralf Stephan, Feb 24 2005
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MATHEMATICA
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a[n_] := Sum[(-1)^(n - k + 1) * StirlingS2[n + 1, k + 1] * ((-1)^k * k! * Subfactorial[-k - 1] - Subfactorial[-1]), {k, 0, n}]; Table[a[n] // FullSimplify, {n, 1, 26}] (* Jean-François Alcover, Jan 09 2014, after Vladeta Jovovic *)
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PROG
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(PARI) a(n)=local(A, B); if(n<0, 0, A=exp(-x+x*O(x^n)); B=exp(A-1); n!*polcoeff(-intformal(B)*A/B, n))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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