login
Logarithm of e.g.f. for primes.
(Formerly M0159)
10

%I M0159 #22 Oct 30 2020 14:56:50

%S 2,-1,3,-12,59,-354,2535,-21190,202731,-2183462,26130441,-343956264,

%T 4938891841,-76827253854,1287026203647,-23100628140676,

%U 442271719973507,-8996704216880580,193776558133638811,-4405549734148088108,105432710994387193283,-2649353692976978990070

%N Logarithm of e.g.f. for primes.

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

%H Alois P. Heinz, <a href="/A007447/b007447.txt">Table of n, a(n) for n = 1..438</a>

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

%p a:= proc(n) option remember; (t-> `if`(n=0, 0, t(n) -add(j*

%p binomial(n, j)*t(n-j)*a(j), j=1..n-1)/n))(i->ithprime(i))

%p end:

%p seq(a(n), n=1..25); # _Alois P. Heinz_, Mar 06 2018

%t 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 Array[a, 25] (* _Jean-François Alcover_, Oct 30 2020, after _Alois P. Heinz_ *)

%Y Cf. A000040, A007446.

%K sign

%O 1,1

%A _N. J. A. Sloane_.

%E Signs from _Christian G. Bower_, Nov 15 1998