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 A330199 Expansion of e.g.f. Product_{k>=1} exp(1 - exp(x^k)). 6
 1, -1, -2, 1, 1, 98, -39, 3225, 1226, 6459, 12473, 821830, -214739887, -201448561, -8997850614, -514986723363, -1310942141971, -26465356716946, -931753364233567, -1858534483400559, 167210272584038942, -7112146717031426801, 312288595642509829797 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..450 FORMULA E.g.f.: A(x) = Product_{k>=1} B(x^k), where B(x) = e.g.f. of complementary Bell numbers (A000587). E.g.f.: exp(-Sum_{j>=1} Sum_{i>=1} x^(i*j) / i!). a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n-1,k-1) * A057625(k) * a(n-k). MATHEMATICA nmax = 22; CoefficientList[Series[Product[Exp[1 - Exp[x^k]], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n - 1, k - 1] k! DivisorSum[k, 1/#! &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}] CROSSREFS Cf. A000587, A057625, A209903. Sequence in context: A173890 A159767 A169658 * A336810 A178473 A164810 Adjacent sequences:  A330196 A330197 A330198 * A330200 A330201 A330202 KEYWORD sign AUTHOR Ilya Gutkovskiy, Dec 05 2019 STATUS approved

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)