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%I #8 Mar 04 2018 03:16:01
%S 1,2,6,23,108,601,3874,28448,234903,2158498,21883451,243025718,
%T 2938265815,38469994687,542905969228,8224586470983,133260591917731,
%U 2301776455966976,42258406133001866,822404997883448574
%N Row sums of triangle A112500.
%F a(n) = Sum_{k=1..n+1} A112500(n, k), n >= 0.
%F G.f: Sum_{n>=1} x^(n-1)/(Product_{k=1..n} (1 - k*x)^(n-k+1)). - _Paul D. Hanna_, Feb 16 2010
%e Contribution from _Paul D. Hanna_, Feb 16 2010: (Start)
%e G.f. A(x) = 1 + 2*x + 6*x^2 + 23*x^3 + 108*x^4 + 601*x^5 + ...
%e A(x) = 1/(1-x) + x/[(1-x)^2*(1-2x)] + x^2/[(1-x)^3*(1-2x)^2*(1-3x)] + ... (End)
%o (PARI) {a(n)=polcoeff(sum(m=1,16,x^(m-1)/prod(k=1,m,(1-k*x +x*O(x^n))^(m-k+1))),n)} \\ _Paul D. Hanna_, Feb 16 2010
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Oct 14 2005