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Column 1 of triangle A134090.
4

%I #3 Mar 30 2012 18:37:07

%S 1,2,9,46,285,2021,16023,139812,1326111,13544857,147880458,1715413558,

%T 21036674321,271585117428,3677831536291,52081368845176,

%U 769123715337395,11816582501728389,188470925178659344,3114771205613655362

%N Column 1 of triangle A134090.

%C 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 a(n) = [x^n] Sum_{k=0..n+1} C(n+1,k)*x^k/(1-k*x) / [Product_{i=1..k}(1-i*x)].

%o (PARI) a(n)=polcoeff(sum(k=0,n+1,binomial(n+1,k)*x^k/(1-k*x)/prod(i=0,k,1-i*x +x*O(x^n))),n)

%Y Cf. A134090; columns: A122455, A134092, A134093; A134094 (row sums); A048993 (S2).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 07 2007