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%I #16 Apr 24 2024 06:06:27
%S 1,6,55,600,7946,123480,2208492,44710272,1011177360,25274905920,
%T 692042185440,20602098316800,662620120237440,22898921925035520,
%U 846245264387040000,33303963647943475200,1390631677349880268800,61407154400075559936000,2859166138267857522585600
%N Product of n!, n-th Pell number and n-th harmonic number.
%F E.g.f.: (2*x*log(-x^2-2*x+1)+(sqrt(2)-sqrt(2)*x)*log(-((sqrt(2)+1)*x-1) / ((sqrt(2)-1)*x+1)))/(4*(x^2+2*x-1)).
%F a(n) = n!*A000129(n)*A001008(n)/A002805(n).
%F D-finite with recurrence 8*a(n) +16*(-2*n+1)*a(n-1) +(16*n^2-32*n+25)*a(n-2) +4*(8*n^3-36*n^2+47*n-13)*a(n-3) +2*(2*n-5)*(2*n^3-11*n^2+17*n-7)*a(n-4) +4*(n-4)^3*a(n-5) +(n-4)^2*(n-5)^2*a(n-6)=0. - _R. J. Mathar_, Apr 24 2024
%Y Cf. A000129, A000142, A000254, A001008, A002805, A052631.
%K nonn
%O 1,2
%A _Vladimir Kruchinin_, Apr 22 2024