A111541 - OEIS

%I #5 Jun 13 2017 22:31:55

%S 0,1,0,3,2,0,14,5,3,0,84,22,8,4,0,600,128,36,12,5,0,4908,896,212,58,

%T 17,6,0,44952,7220,1496,360,90,23,7,0,454344,65336,12128,2652,602,134,

%U 30,8,0,5016768,653720,110288,22320,4736,974,192,38,9,0,60062352,7155104

%N Matrix logarithm of triangle A111536.

%C Column 0 (A111538) is found in column 2 of triangle A111536.

%e Triangle begins:

%e 0;

%e 1,0;

%e 3,2,0;

%e 14,5,3,0;

%e 84,22,8,4,0;

%e 600,128,36,12,5,0;

%e 4908,896,212,58,17,6,0;

%e 44952,7220,1496,360,90,23,7,0;

%e 454344,65336,12128,2652,602,134,30,8,0;

%e 5016768,653720,110288,22320,4736,974,192,38,9,0; ...

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

%Y Cf. A111536, A111538 (column 0), A111542 (column 1), A111543 (column 2).

%K nonn,tabl

%O 0,4

%A _Paul D. Hanna_, Aug 06 2005