A129587 a(n) = n!*((1 + 3n + n^2)*H(n) - n), where H(n) is the n-th harmonic number.

4, 29, 191, 1354, 10634, 92700, 892548, 9430416, 108630864, 1356063840, 18245210400, 263298142080, 4057825368960, 66527793642240, 1156298057913600, 21239191491840000, 411134620109875200, 8365635747476582400

Offset: 1

Author

Paul Curtz, May 30 2007

Keywords

• nonn
• less

Comments

The numbers can be generated from row sums from coefficients of the polynomials Sum_{i=1..n} ((n+1)^2 - 1 + (n+1-i)*z^n)*z^(i-1)/i.

The coefficients written as an array of 2n numbers in row n for the first 5 polynomials are

3 1 <- 3+z

8 4 2 1/2 <- 8+4z+2z^2+z^3/2

15 15/2 5 3 1 1/3

24 12 8 6 4 3/2 2/3 1/4

35 35/2 35/3 35/4 7 5 2 1 1/2 1/5

These rows multiplied by n! are

3 1

16 8 4 1

90 45 30 18 6 2

576 288 192 144 96 36 16 6

4200 2100 1400 1050 840 600 240 120 60 24

where the first column is A129326. The latter row sums define a(n), which are n! times the polynomials evaluated at z=1.

Crossrefs

Cf. A001008, A002805, A129326.

Programs

Mathematica

Array[#!*((1+3#+#^2)*HarmonicNumber[#]-#)&,18] (* James C. McMahon, Jan 31 2025 *)

Extensions

Edited and corrected by R. J. Mathar, Jul 27 2008