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%I #14 May 09 2022 00:34:20
%S 0,1,7,77,1222,26364,739608,26079780,1125791280,58257484128,
%T 3552890064480,251777905728480,20488109614761600,1895120214639868800,
%U 197527783071095930880,23023412842885582176000,2980946191374310495795200,426192103002275699198054400
%N a(n) = n-th second-order hyperharmonic-exponential number, multiplied by n!.
%H Ayhan Dil and Veli Kurt, <a href="https://www.emis.de/journals/INTEGERS/papers/m38/m38.Abstract.html">Polynomials related to harmonic numbers and evaluation of harmonic number series I</a>, INTEGERS, 12 (2012), #A38.
%F a(n) = (Sum_{k=0..n} A008277(n,k) * H2(k)) * A000142(n) where H2(k) is defined by g.f.: - log(1-x)/(1-x)^2. - _Michel Marcus_, Feb 09 2013
%o (PARI)
%o hyp(n,alpha) = {x= y+O(y^(n+1)); gf = - log(1-x)/(1-x)^alpha; polcoeff(gf, n, y);}
%o a(n, alpha=2) = sum(k=0, n, n!*(sum(i=0, k, (-1)^i*binomial(k, i)*i^n)*(-1)^k/k!)*hyp(k,alpha));
%o \\ _Michel Marcus_, Feb 09 2013
%Y Cf. A000142, A008277.
%K nonn
%O 0,3
%A _Michel Marcus_, following a suggestion of _N. J. A. Sloane_ , Feb 09 2013
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