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A308645
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Expansion of e.g.f. exp(1 + x - exp(2*x)).
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2
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1, -1, -3, 3, 41, 87, -571, -5701, -14575, 156655, 2094925, 9148851, -63364423, -1474212665, -11494853995, 10945362411, 1520718442785, 20719421344991, 100137575499165, -1638818071763869, -45333849658449847, -512404024891840969, -577060092568365467, 99142586163648127771
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = exp(1) * Sum_{k>=0} (-1)^k*(2*k + 1)^n/k!.
a(n) = Sum_{k=0..n} binomial(n,k)*2^k*A000587(k).
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MATHEMATICA
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nmax = 23; CoefficientList[Series[Exp[1 + x - Exp[2 x]], {x, 0, nmax}], x] Range[0, nmax]!
Table[Exp[1] Sum[(-1)^k (2 k + 1)^n/k!, {k, 0, Infinity}], {n, 0, 23}]
Table[Sum[Binomial[n, k] 2^k BellB[k, -1], {k, 0, n}], {n, 0, 23}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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