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 A134093 Column 3 of triangle A134090. 4

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

%S 1,4,30,215,1729,15176,143814,1462995,15876410,182811992,2223580281,

%T 28458251185,381943459065,5359649816728,78430018675440,

%U 1194057733357517,18873870914263424,309154787519651284,5238840625331179517

%N Column 3 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+3} C(n+3,k)*x^k/(1-k*x)^3 / [Product_{i=1..k}(1-i*x)].

%o (PARI) {a(n)= polcoeff(sum(k=0,n+3,binomial(n+3,k)*x^k/(1-k*x)^3/prod(i=0,k,1-i*x +x*O(x^n))),n)}

%Y Cf. A134090; columns: A122455, A134091, A134092; A134094 (row sums); A048993 (S2).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 08 2007

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Last modified August 15 04:38 EDT 2024. Contains 375172 sequences. (Running on oeis4.)