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%I #22 Jan 18 2024 06:36:37
%S 1,2,5,14,44,158,663,3310,19759,139660,1147120,10729684,112309193,
%T 1297522650,16371057801,223716758346,3289199827236,51745234494858,
%U 867023125576027,15411557297930534,289610871340870883,5736017561257017128,119413599371241577016
%N A084938 * [1,2,3,...], where A084938 is taken as lower triangular matrix.
%H Alois P. Heinz, <a href="/A134378/b134378.txt">Table of n, a(n) for n = 0..170</a>
%F a(n) ~ 2 * (n-1)! * (1 + 3/n + 12/n^2 + 58/n^3 + 327/n^4 + 2107/n^5 + 15329/n^6 + 125041/n^7 + 1139467/n^8 + 11582187/n^9 + 131230827/n^10). - _Vaclav Kotesovec_, Mar 17 2015
%e a(4) = 44 = (0, 6, 5, 3, 1) dot (1, 2, 3, 4, 5) = (0 + 12 + 15 + 12 + 5).
%p series((1-x*hypergeom([1,1],[],x))^(-2), x=0, 50); # appears to generate the sequence - _Mark van Hoeij_, Apr 22 2013
%t CoefficientList[Series[1/(1-x*HypergeometricPFQ[{1, 1}, {}, x])^2, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 17 2015 after _Mark van Hoeij_ *)
%t CoefficientList[Assuming[Element[x,Reals], Series[E^(2/x)/(ExpIntegralEi[1/x]-E^(1/x))^2, {x,0,25}]],x] (* _Vaclav Kotesovec_, Aug 03 2015 *)
%Y Cf. A084938, A260532.
%K nonn
%O 0,2
%A _Gary W. Adamson_, Oct 22 2007, corrected Oct 26 2007
%E More terms from _Alois P. Heinz_, Apr 27 2012