Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Dec 17 2019 05:50:42
%S 4,29,191,1354,10634,92700,892548,9430416,108630864,1356063840,
%T 18245210400,263298142080,4057825368960,66527793642240,
%U 1156298057913600,21239191491840000,411134620109875200,8365635747476582400
%N a(n) = n!*((1 + 3n + n^2)*H(n) - n), where H(n) is the n-th harmonic number.
%C 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 The coefficients written as an array of 2n numbers in row n for the first 5 polynomials are
%C 3 1 <- 3+z
%C 8 4 2 1/2 <- 8+4z+2z^2+z^3/2
%C 15 15/2 5 3 1 1/3
%C 24 12 8 6 4 3/2 2/3 1/4
%C 35 35/2 35/3 35/4 7 5 2 1 1/2 1/5
%C These rows multiplied by n! are
%C 3 1
%C 16 8 4 1
%C 90 45 30 18 6 2
%C 576 288 192 144 96 36 16 6
%C 4200 2100 1400 1050 840 600 240 120 60 24
%C where the first column is A129326. The latter row sums define a(n), which are n! times the polynomials evaluated at z=1.
%Y Cf. A001008, A002805, A129326.
%K nonn,less
%O 1,1
%A _Paul Curtz_, May 30 2007
%E Edited and corrected by _R. J. Mathar_, Jul 27 2008