A117271
Column 0 of triangle A117270, which is the matrix log of triangle A117269.
Original entry on oeis.org
0, 1, 2, 12, 134, 2100, 42302, 1041852, 30331814, 1019056260, 38805685262, 1651676734092, 77703508288694, 4003868870257620, 224255353667365022, 13565588100060643932, 881405810330856632774, 61218510507062012550180
Offset: 0
-
{a(n)=local(C=matrix(n+1,n+1,r,c,if(r>=c,binomial(r-1,c-1))),M=C,L); for(i=1,n+1,M=(M-M^0)^2+C);L=sum(r=1,#M,-(M^0-M)^r/r);return(L[n+1,1])}
A117269
Triangle T, read by rows, that satisfies matrix equation: T - (T-I)^2 = C, where C is Pascal's triangle.
Original entry on oeis.org
1, 1, 1, 3, 2, 1, 19, 9, 3, 1, 207, 76, 18, 4, 1, 3211, 1035, 190, 30, 5, 1, 64383, 19266, 3105, 380, 45, 6, 1, 1581259, 450681, 67431, 7245, 665, 63, 7, 1, 45948927, 12650072, 1802724, 179816, 14490, 1064, 84, 8, 1, 1541641771, 413540343, 56925324, 5408172
Offset: 0
Triangle T begins:
1;
1,1;
3,2,1;
19,9,3,1;
207,76,18,4,1;
3211,1035,190,30,5,1;
64383,19266,3105,380,45,6,1;
1581259,450681,67431,7245,665,63,7,1; ...
where (T-I)^2 =
0;
0,0;
2,0,0;
18,6,0,0;
206,72,12,0,0;
3210,1030,180,20,0,0;
64382,19260,3090,360,30,0,0; ...
and T - (T-I)^2 = Pascal's triangle.
-
{T(n,k)=local(C=matrix(n+1,n+1,r,c,if(r>=c,binomial(r-1,c-1))),M=C); for(i=1,n+1,M=(M-M^0)^2+C);return(M[n+1,k+1])}
Showing 1-2 of 2 results.
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