cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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

Views

Author

Seiichi Manyama, Oct 30 2017

Keywords

Crossrefs

Main diagonal of A294296.
Cf. A252782.

Programs

  • Mathematica
    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

Views

Author

Seiichi Manyama, Nov 11 2017

Keywords

Examples

			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, ...
		

Crossrefs

Columns k=0..2 give A023881, A023882, A294813.
Rows n=0+1, 2 give A000012, A000051(n+1).

Formula

G.f. of column k: Product_{j>0} 1/(1 - j^j*x^j)^(j^(k-1)).
Showing 1-2 of 2 results.