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A128602 Row sums of triangle A128567. 3

%I

%S 1,3,12,60,315,1869,11472,74797,502908,3505031,24973089,182208083,

%T 1352620790,10207771213,78082422354,604699597868,4733082767467,

%U 37406134058641,298165102770381,2395219866441531,19376637845028027,157757577529194488,1291926016200778464

%N Row sums of triangle A128567.

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

%F a(n) = Sum_{s=0..n-1} A047812(n,s)*A000108(s+1) for n >= 1. - _Petros Hadjicostas_, May 31 2020

%o (PARI) {a(n)=local(M);M=matrix(n+1,n+1,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)))); sum(k=0,n,(M^2)[n+1,k+1])}

%o /* To display results because the offset was changed: */

%o vector(28, n, a(n-1)) \\ _Petros Hadjicostas_, May 31 2020

%Y Cf. A000108, A047812, A128567, A128568 (column 1), A128569 (column 2).

%K nonn

%O 1,2

%A _Paul D. Hanna_, Mar 12 2007

%E Offset changed by _Petros Hadjicostas_, May 31 2020 to agree with A128567

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Last modified March 7 19:13 EST 2021. Contains 341928 sequences. (Running on oeis4.)