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A300661
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Expansion of e.g.f. exp(-Sum_{k>=1} prime(k)*x^k/k!).
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1
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1, -2, 1, 5, 4, -53, -177, 282, 5759, 20355, -83420, -1420133, -6245485, 29035652, 648899541, 4034393367, -10488623858, -464971765297, -4310935438663, -3489419105786, 446500913437911, 6423072226704027, 30987397708208720, -462727554963927783, -11862200720684515159
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: exp(-Sum_{k>=1} A000040(k)*x^k/k!).
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EXAMPLE
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E.g.f.: A(x) = 1 - 2*x/1! + x^2/2! + 5*x^3/3! + 4*x^4/4! - 53*x^5/5! - 177*x^6/6! + 282*x^7/7! + ...
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, -add(a(n-j)*
ithprime(j)*binomial(n-1, j-1), j=1..n))
end:
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MATHEMATICA
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nmax = 24; CoefficientList[Series[Exp[-Sum[Prime[k] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[-Prime[k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 24}]
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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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