A237872 Numerator of Sum_{i=1..n} n^i/i.

1, 4, 33, 292, 10085, 48756, 2827293, 257063528, 13779684369, 70889442280, 72634140523901, 314690934778068, 140915129117772841, 5533416685634616884, 251767541303505518145, 55644156684309383260624, 7481965178603932789388755

Offset: 1

Author

Bruno Berselli, Feb 14 2014

Keywords

• nonn
• frac

Comments

The sequence gives the numerators of -n^(n+1)*Phi(n,1,n+1)-log(-n+1) for n>1, where Phi is the Lerch transcendent.

Links

• Bruno Berselli, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A236772, A237873 (denominators).

Programs

Magma

terms:=20; s:=[&+[n^i/i: i in [1..n]]: n in [1..terms]]; [Numerator(s[n]): n in [1..terms]];

Maple

A237872:=n->numer(add(n^i/i, i=1..n)): seq(A237872(n), n=1..20); # Wesley Ivan Hurt, Apr 26 2017

Mathematica

f[n_] := Sum[n^i/i, {i, 1, n}]; Table[Numerator[f[n]], {n, 1, 20}]