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A128569 Column 2 of triangle A128567. 3


%S 1,14,117,813,4871,27743,151208,804065,4185683,21472005,108766010,

%T 545507633,2712801330,13394412999,65722444172,320721839860,

%U 1557502222385,7530671086667,36267851679585,174038009185816,832392015517829,3969017685816667,18871416851149078

%N Column 2 of triangle A128567.

%C A128567 is the matrix square of Parker's partition triangle A047812.

%F a(n) = Sum_{s=2..n+2} A047812(n+3,s)*A047812(s+1,2) for n >= 0. - _Petros Hadjicostas_, May 31 2020

%o (PARI) {a(n)=local(M);M=matrix(n+3,n+3,r,c,if(r<c,0,if(r==0,1, polcoeff(prod(j=r+1,2*r,1-q^j)/prod(j=1,r,1-q^j),(r+1)*(c-1), q)))); (M^2)[n+3,3]}

%Y Cf. A047812, A128567, A128568 (column 1), A128602 (row sums).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 12 2007

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Last modified January 16 15:53 EST 2021. Contains 340206 sequences. (Running on oeis4.)