A354593 Decimal expansion of Sum_{k>=1} (1 - log(k)/k)^(3*k).

1, 1, 0, 9, 8, 1, 2, 3, 5, 1, 6, 7, 2, 7, 4, 0, 9, 0, 2, 5, 9, 7, 7, 2, 3, 0, 0, 5, 6, 8, 6, 1, 6, 4, 7, 7, 9, 3, 8, 0, 1, 6, 3, 2, 5, 6, 1, 0, 3, 3, 4, 2, 3, 8, 6, 7, 9, 2, 0, 8, 1, 3, 4, 8, 4, 1, 9, 8, 3, 1, 0, 9, 3, 6, 0, 1, 2, 2, 5, 5, 7, 4, 1, 4, 4, 0, 2, 2, 5, 4, 5, 2, 0, 9, 9, 8, 8, 3, 9, 4, 0, 4, 5, 3, 8

Offset: 1

Author

Vaclav Kotesovec, Jun 01 2022

Keywords

• nonn
• cons

Examples

			1.109812351672740902597723005686164779380163256103342386792081348419831...
		

Crossrefs

Cf. A354450, A354592.

Programs

Maple

Digits := 120: ser := sort(convert(series((1-log(n)/n)^(3*n), n = infinity, 300), polynom), n): s := evalf(sum(op(1, ser), n = 1..infinity) + sum(op(2, ser), n = 1..infinity), 120): for k from 3 to nops(ser) do serx := expand(op(k, ser)): for j to nops(serx) do s := s + evalf(sum(op(j, serx), n = 1..infinity), 120) end do: print(k, s) end do:

Mathematica

NSum[(1 - Log[k]/k)^(3*k), {k, 1, Infinity}, WorkingPrecision -> 40, NSumTerms -> 1000]

PARI

sumpos(k=1, (1 - log(k)/k)^(3*k)) \\ Michel Marcus, Jun 01 2022