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Column 2 of triangle A134090.
4

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

%S 1,3,18,110,780,6167,53494,504030,5112090,55411697,638154165,

%T 7770348170,99618149267,1339889000543,18848892749144,276573551651632,

%U 4222814264496510,66947348027905977,1099955438013660173

%N Column 2 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+2} C(n+2,k)*x^k/(1-k*x)^2 / [Product_{i=1..k}(1-i*x)].

%o (PARI) {a(n)= polcoeff(sum(k=0,n+2,binomial(n+2,k)*x^k/(1-k*x)^2/prod(i=0,k,1-i*x +x*O(x^n))),n)}

%Y Cf. A134090; columns: A122455, A134091, A134093; A134094 (row sums); A048993 (S2).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 08 2007