A007447 Logarithm of e.g.f. for primes.

2, -1, 3, -12, 59, -354, 2535, -21190, 202731, -2183462, 26130441, -343956264, 4938891841, -76827253854, 1287026203647, -23100628140676, 442271719973507, -8996704216880580, 193776558133638811, -4405549734148088108, 105432710994387193283, -2649353692976978990070

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..438

Crossrefs

Cf. A000040, A007446.

Programs

Maple

a:= proc(n) option remember; (t-> `if`(n=0, 0, t(n) -add(j*
      binomial(n, j)*t(n-j)*a(j), j=1..n-1)/n))(i->ithprime(i))
    end:
seq(a(n), n=1..25);  # Alois P. Heinz, Mar 06 2018

Mathematica

a[n_] := a[n] = Function[t, If[n==0, 0, t[n] - Sum[j Binomial[n, j] t[n-j] a[j], {j, 1, n-1}]/n]][Prime];
Array[a, 25] (* Jean-François Alcover, Oct 30 2020, after Alois P. Heinz *)

Formula

E.g.f.: log(1 + Sum_{k>=1} prime(k)*x^k/k!). - Ilya Gutkovskiy, Mar 10 2018

Extensions

Signs from Christian G. Bower, Nov 15 1998