Search: id:A134094
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%I A134094
%S A134094 1,2,6,26,140,887,6405,51564,455712,4370567,45081476,496556194,
%T A134094 5806502663,71734434956,932447207866,12707973761320,181033752071568,
%U A134094 2688530124711819,41525910256013832,665674913113633582
%N A134094 Row sums of triangle A134090.
%C A134094 Row n of triangle T=A134090 = row n of (I + D*C)^n for n>=0 where C denotes 
               Pascal's triangle, I the identity matrix and D a matrix where D(n+1,
               n)=1 and zeros elsewhere.
%F A134094 a(n) = [x^n] Sum_{k=0..n} C(n,k)*x^k*(1-k*x) / [Product_{i=0..k+1}(1-i*x)], 
               equivalently, a(n) = Sum_{k=0..n} C(n,k)*[S2(n,k) - k*S2(n-1,k)], 
               where S2(n,k) = A048993(n,k) are Stirling numbers of the 2nd kind.
%o A134094 (PARI) {a(n)=sum(k=0,n,binomial(n,k)*polcoeff((1-k*x)/prod(i=0,k+1,1-i*x+x*O(x^(n))),
               n-k))}
%Y A134094 Cf. A134090; columns: A122455, A134091, A134092, A134093; A048993 (S2).
%Y A134094 Sequence in context: A030957 A030898 A002788 this_sequence A009575 A127116 
               A107404
%Y A134094 Adjacent sequences: A134091 A134092 A134093 this_sequence A134095 A134096 
               A134097
%K A134094 nonn
%O A134094 0,2
%A A134094 Paul D. Hanna (pauldhanna(AT)juno.com), Oct 08 2007

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