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%I #5 Jun 13 2019 12:54:13
%S 1,-1,-3,3,41,87,-571,-5701,-14575,156655,2094925,9148851,-63364423,
%T -1474212665,-11494853995,10945362411,1520718442785,20719421344991,
%U 100137575499165,-1638818071763869,-45333849658449847,-512404024891840969,-577060092568365467,99142586163648127771
%N Expansion of e.g.f. exp(1 + x - exp(2*x)).
%F a(n) = exp(1) * Sum_{k>=0} (-1)^k*(2*k + 1)^n/k!.
%F a(n) = Sum_{k=0..n} binomial(n,k)*2^k*A000587(k).
%t nmax = 23; CoefficientList[Series[Exp[1 + x - Exp[2 x]], {x, 0, nmax}], x] Range[0, nmax]!
%t Table[Exp[1] Sum[(-1)^k (2 k + 1)^n/k!, {k, 0, Infinity}], {n, 0, 23}]
%t Table[Sum[Binomial[n, k] 2^k BellB[k, -1], {k, 0, n}], {n, 0, 23}]
%Y Cf. A000587, A055882, A126390, A308536.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Jun 13 2019
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