A107724 - OEIS

%I #5 Jun 13 2017 01:52:14

%S 0,1,0,4,2,0,31,10,3,0,343,88,19,4,0,4855,1066,199,31,5,0,83209,16216,

%T 2779,382,46,6,0,1670743,295360,47791,6130,655,64,7,0,38436673,

%U 6254824,970849,119182,11929,1036,85,8,0,996825703,150917560,22697647,2703730

%N Matrix logarithm of triangle A107719, read by rows.

%C Also equals one-third of the matrix logarithm of A107717. Column 0 is A107725.

%e Triangle begins:

%e 0;

%e 1,0;

%e 4,2,0;

%e 31,10,3,0;

%e 343,88,19,4,0;

%e 4855,1066,199,31,5,0;

%e 83209,16216,2779,382,46,6,0;

%e 1670743,295360,47791,6130,655,64,7,0;

%e 38436673,6254824,970849,119182,11929,1036,85,8,0; ...

%o (PARI) T(n,k)=local(L,M=matrix(n+1,n+1,m,j,if(m>=j,if(m==j,1,if(m==j+1,-3*j, polcoeff(1/sum(i=0,m-j,prod(r=0,i-1,3*r+1)*x^i)+O(x^m),m-j)))))^-1); L=sum(i=1,#M,(-1)^(i-1)*(M-M^0)^i/i);return(if(n<k || k<0,0,L[n+1,k+1]/3))

%Y Cf. A107717, A107719.

%K nonn,tabl

%O 0,4

%A _Paul D. Hanna_, May 30 2005