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A135892 Triangle, read by rows, equal to P^5, where triangle P = A135880.

%I A135892 #2 Mar 30 2012 18:37:08
%S A135892 1,5,1,30,10,1,220,95,15,1,1945,990,195,20,1,20340,11635,2625,330,25,
%T A135892 1,247066,154450,38270,5440,500,30,1,3430936,2302142,611525,94515,
%U A135892 9750,705,35,1,53741404,38229214,10721093,1761940,196500,15870,945,40,1
%N A135892 Triangle, read by rows, equal to P^5, where triangle P = A135880.
%C A135892 Triangle P = A135880 is defined by: column k of P^2 equals column 0 of P^(2k+2) such that column 0 of P^2 equals column 0 of P shift left.
%F A135892 Column k of P^5 = column 2 of R^(k+1) for k>=0 where triangle R = A135894; column 0 of P^5 = column 2 of R; column 1 of P^5 = column 2 of R^2; column 2 of P^5 = column 2 of R^3; column 3 of P^5 = column 2 of R^4.
%e A135892 Triangle P^5 begins:
%e A135892 1;
%e A135892 5, 1;
%e A135892 30, 10, 1;
%e A135892 220, 95, 15, 1;
%e A135892 1945, 990, 195, 20, 1;
%e A135892 20340, 11635, 2625, 330, 25, 1;
%e A135892 247066, 154450, 38270, 5440, 500, 30, 1;
%e A135892 3430936, 2302142, 611525, 94515, 9750, 705, 35, 1;
%e A135892 53741404, 38229214, 10721093, 1761940, 196500, 15870, 945, 40, 1;
%e A135892 938816814, 701685738, 205607124, 35429974, 4182295, 363820, 24115, 1220, 45, 1;
%e A135892 where P = A135880 begins:
%e A135892 1;
%e A135892 1, 1;
%e A135892 2, 2, 1;
%e A135892 6, 7, 3, 1;
%e A135892 25, 34, 15, 4, 1;
%e A135892 138, 215, 99, 26, 5, 1;
%e A135892 970, 1698, 814, 216, 40, 6, 1; ...
%e A135892 in which column k of P = column 0 of R^(k+1),
%e A135892 where R = A135894 begins:
%e A135892 1;
%e A135892 1, 1;
%e A135892 2, 3, 1;
%e A135892 6, 12, 5, 1;
%e A135892 25, 63, 30, 7, 1;
%e A135892 138, 421, 220, 56, 9, 1;
%e A135892 970, 3472, 1945, 525, 90, 11, 1; ...
%e A135892 in which column k of R equals column 0 of P^(2k+1).
%o A135892 (PARI) {T(n,k)=local(P=Mat(1),R,PShR);if(n>0,for(i=0,n, 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^5)[n+1,k+1]}
%Y A135892 Cf. A135880 (P), A135894 (R), A135895 (R^2), A135896 (R^3), A135897 (R^4).
%K A135892 nonn,tabl
%O A135892 0,2
%A A135892 _Paul D. Hanna_, Dec 15 2007