A135887 Column 2 of triangle Q = A135885; also equals column 0 of Q^3 = A135893.

1, 6, 42, 351, 3470, 39968, 528306, 7906598, 132426050, 2457643895, 50110693656, 1114365815786, 26856942480503, 697612318151050, 19435260247394150, 578255661792065917, 18303904706366202568, 614296560055922433760

Offset: 0

Author

Paul D. Hanna, Dec 15 2007

Keywords

• nonn

Examples

			Triangle Q = A135885 begins:
1;
2, 1;
6, 4, 1;
25, 20, 6, 1;
138, 126, 42, 8, 1;
970, 980, 351, 72, 10, 1;
8390, 9186, 3470, 748, 110, 12, 1; ...
where column k of Q equals column 0 of Q^(k+1) such that
column 0 of Q equals column 0 of P=A135880 shift left and Q=P^2.
		

Crossrefs

Cf. A135885 (Q), A135893 (Q^3), A135880; other columns: A135881, A135886.

Programs

PARI

{a(n)=local(P=Mat(1),R,PShR);if(n==0,1,for(i=0,n+1, PShR=matrix(#P,#P, r,c, if(r>=c,if(r==c,1,if(c==1,0,P[r-1,c-1]))));R=P*PShR; R=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,R[r,c], if(c==1,(P^2)[ #P,1],(P^(2*c-1))[r-c+1,1])))); P=matrix(#R, #R, r,c, if(r>=c, if(r<#R,P[r,c], (R^c)[r-c+1,1]))));(P^2)[n+3,3])}