A294388
a(n) = n! * [x^n] exp(Sum_{k=1..n} sigma_n(k) * x^k).
Original entry on oeis.org
1, 1, 11, 223, 12193, 1548841, 501460531, 355752425239, 558112176198305, 2023318561014654769, 15928875457207423721731, 268023268481704204728199711, 10084410400965244525857478169665, 817174553170437003290060071895273113
Offset: 0
-
Table[n! * SeriesCoefficient[Exp[Sum[DivisorSigma[n,k] * x^k, {k,1,n}]],{x,0,n}], {n,0,20}] (* Vaclav Kotesovec, Aug 30 2025 *)
A294946
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of exp(Sum_{j>0} sigma_k(j)*x^j/j) in powers of x.
Original entry on oeis.org
1, 1, 1, 1, 1, 3, 1, 1, 5, 12, 1, 1, 9, 32, 82, 1, 1, 17, 90, 304, 725, 1, 1, 33, 260, 1162, 3537, 8811, 1, 1, 65, 762, 4516, 17435, 52010, 128340, 1, 1, 129, 2252, 17722, 86529, 310193, 895397, 2257687, 1, 1, 257, 6690, 69964, 431675, 1865766, 6286826, 18016416, 45658174
Offset: 0
Square array begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
3, 5, 9, 17, 33, ...
12, 32, 90, 260, 762, ...
82, 304, 1162, 4516, 17722, ...
725, 3537, 17435, 86529, 431675, ...
Showing 1-2 of 2 results.