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%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