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

%I A007447 M0159 #26 Jul 08 2025 17:04:38
%S A007447 2,-1,3,-12,59,-354,2535,-21190,202731,-2183462,26130441,-343956264,
%T A007447 4938891841,-76827253854,1287026203647,-23100628140676,
%U A007447 442271719973507,-8996704216880580,193776558133638811,-4405549734148088108,105432710994387193283,-2649353692976978990070
%N A007447 Logarithm of e.g.f. for primes.
%D A007447 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007447 Alois P. Heinz, <a href="/A007447/b007447.txt">Table of n, a(n) for n = 1..438</a>
%F A007447 E.g.f.: log(1 + Sum_{k>=1} prime(k)*x^k/k!). - _Ilya Gutkovskiy_, Mar 10 2018
%p A007447 a:= proc(n) option remember; (t-> `if`(n=0, 0, t(n) -add(j*
%p A007447       binomial(n, j)*t(n-j)*a(j), j=1..n-1)/n))(i->ithprime(i))
%p A007447     end:
%p A007447 seq(a(n), n=1..25);  # _Alois P. Heinz_, Mar 06 2018
%t A007447 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];
%t A007447 Array[a, 25] (* _Jean-François Alcover_, Oct 30 2020, after _Alois P. Heinz_ *)
%Y A007447 Cf. A000040, A007446.
%K A007447 sign
%O A007447 1,1
%A A007447 _N. J. A. Sloane_
%E A007447 Signs from _Christian G. Bower_, Nov 15 1998