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A187548 Alternating partial sums of L(n)*H(n+1), product of central Lah number L(n) and Harmonic number H(n+1).

%I A187548 #11 Feb 01 2019 01:20:45
%S A187548 1,2,64,2436,131824,9203264,787735648,79884060128,9366719620672,
%T A187548 1246887723480128,185786630586649792,30635253866287585088,
%U A187548 5538860010787064796352,1089574788981508858403648,231683608824013918904796352,52954849085008593516185123648
%N A187548 Alternating partial sums of L(n)*H(n+1), product of central Lah number L(n) and Harmonic number H(n+1).
%F A187548 a(n) = Sum_{k=0..n} (-1)^(n-k)*A187547(k).
%p A187548 H := proc(n) add(1/i,i=1..n) ; end proc:
%p A187548 A187535 := proc(n) if n=0 then 1; else binomial(2*n-1, n-1)*(2*n)!/n! end if; end proc:
%p A187548 A187547 := proc(n) H(n+1)*A187535(n) ; end proc:
%p A187548 A187548 := proc(n) add( A187547(k)*(-1)^(n-k),k=0..n) ; end proc:
%p A187548 seq(A187548(n),n=0..20) ; # _R. J. Mathar_, Mar 24 2011
%t A187548 Table[Sum[(-1)^n+(-1)^(n-k)Binomial[2k-1,k-1](2k)!/k!HarmonicNumber[k+1],{k,1,n}],{n,0,12}]
%o A187548 (Maxima) makelist((-1)^n+sum((-1)^(n-k)*binomial(2*k-1,k-1)*(2*k)!/k!*sum(1/i,i,1,k+1),k,1,n),n,0,12);
%Y A187548 Cf. A187535, A001008, A187547.
%K A187548 nonn,easy
%O A187548 0,2
%A A187548 _Emanuele Munarini_, Mar 11 2011