# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a135081 Showing 1-1 of 1 %I A135081 #7 Mar 30 2012 18:37:07 %S A135081 1,1,2,8,50,436,4912,68098,1122952,21488640,468331252,11456367820, %T A135081 310888085872,9269621420284,301268634277760,10601062978739338, %U A135081 401550210033474420,16291237867482727084,704847239600911931248 %N A135081 Column 0 of triangle A135080. %C A135081 Triangle A135080 transforms diagonals in the table of coefficients of successive iterations of x+x^2 (cf. A122888). %C A135081 Triangle A187005 is defined by: A187005(n,k) = [y^k] R_{n-1}(y+y^2) for k=1..n where R_n(y) is the n-th row polynomial for n>1 with R_1(y)=y. %H A135081 Paul D. Hanna, Table of n, a(n) for n=0..50 %F A135081 Equals the main diagonal of triangle A187005. %o A135081 (PARI) /* As column 0 of triangle A135080 (slower): */ %o A135081 {a(n)=local(F=x,M,N,P); M=matrix(n+2,n+2,r,c,F=x;for(i=1,r+c-2,F=subst(F,x,x+x^2+x*O(x^(n+2))));polcoeff(F,c)); N=matrix(n+1,n+1,r,c,M[r,c]);P=matrix(n+1,n+1,r,c,M[r+1,c]);(P~*N~^-1)[n+1,1]} %o A135081 (PARI) /* As the main diagonal of triangle A187005 (faster): */ %o A135081 {a(n)=local(Rn=y); for(m=1, n+1, Rn=subst(truncate(Rn), y, y+y^2+y*O(y^m))); polcoeff(Rn/y, n, y)} %Y A135081 Cf. A135080 (triangle); other columns: A135082, A135083. %Y A135081 Cf. A187005, A187006, A187007, A187008, A187009. %K A135081 nonn %O A135081 0,3 %A A135081 _Paul D. Hanna_, Nov 18 2007 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE