a(n) = Sum_{k=0..n-1} (-1)^k*k*A000172(k).

Terms

a(0) =0a(1) =0a(2) =-2a(3) =18a(4) =-150a(5) =1234a(6) =-10026a(7) =81078a(8) =-653642a(9) =5259654a(10) =-42268734a(11) =339383866a(12) =-2723191254a(13) =21839901546a(14) =-175088593334