A007447 Logarithm of e.g.f. for primes. (Formerly M0159)

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

Offset

1,1

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

Formula

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

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 *)

Crossrefs

Cf. A000040, A007446.

Sequence in context: A317548 A320327 A366591 * A153189 A362272 A095852

Adjacent sequences: A007444 A007445 A007446 * A007448 A007449 A007450

Keyword

sign

Author

N. J. A. Sloane.

Extensions

Signs from Christian G. Bower, Nov 15 1998

Status

approved