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.
%I A129587 #13 Feb 01 2025 08:47:03
%S A129587 4,29,191,1354,10634,92700,892548,9430416,108630864,1356063840,
%T A129587 18245210400,263298142080,4057825368960,66527793642240,
%U A129587 1156298057913600,21239191491840000,411134620109875200,8365635747476582400
%N A129587 a(n) = n!*((1 + 3n + n^2)*H(n) - n), where H(n) is the n-th harmonic number.
%C A129587 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.
%C A129587 The coefficients written as an array of 2n numbers in row n for the first 5 polynomials are
%C A129587 3 1 <- 3+z
%C A129587 8 4 2 1/2 <- 8+4z+2z^2+z^3/2
%C A129587 15 15/2 5 3 1 1/3
%C A129587 24 12 8 6 4 3/2 2/3 1/4
%C A129587 35 35/2 35/3 35/4 7 5 2 1 1/2 1/5
%C A129587 These rows multiplied by n! are
%C A129587 3 1
%C A129587 16 8 4 1
%C A129587 90 45 30 18 6 2
%C A129587 576 288 192 144 96 36 16 6
%C A129587 4200 2100 1400 1050 840 600 240 120 60 24
%C A129587 where the first column is A129326. The latter row sums define a(n), which are n! times the polynomials evaluated at z=1.
%t A129587 Array[#!*((1+3#+#^2)*HarmonicNumber[#]-#)&,18] (* _James C. McMahon_, Jan 31 2025 *)
%Y A129587 Cf. A001008, A002805, A129326.
%K A129587 nonn,less
%O A129587 1,1
%A A129587 _Paul Curtz_, May 30 2007
%E A129587 Edited and corrected by _R. J. Mathar_, Jul 27 2008