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A135891 Triangle, read by rows, equal to P^4, where triangle P = A135880; also equals Q^2, where triangle Q = P^2 = A135885.

%I A135891 #2 Mar 30 2012 18:37:08
%S A135891 1,4,1,20,8,1,126,64,12,1,980,580,132,16,1,9186,6064,1554,224,20,1,
%T A135891 101492,72832,20260,3240,340,24,1,1296934,995050,294218,50496,5830,
%U A135891 480,28,1,18868652,15301004,4745522,857840,105620,9516,644,32,1,308478492
%N A135891 Triangle, read by rows, equal to P^4, where triangle P = A135880; also equals Q^2, where triangle Q = P^2 = A135885.
%F A135891 Column k of Q^2 = column 1 of Q^(k+1) for k>=0 where triangle Q = P^2 = A135885. 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.
%e A135891 Triangle P^4 = Q^2 begins:
%e A135891 1;
%e A135891 4, 1;
%e A135891 20, 8, 1;
%e A135891 126, 64, 12, 1;
%e A135891 980, 580, 132, 16, 1;
%e A135891 9186, 6064, 1554, 224, 20, 1;
%e A135891 101492, 72832, 20260, 3240, 340, 24, 1;
%e A135891 1296934, 995050, 294218, 50496, 5830, 480, 28, 1;
%e A135891 18868652, 15301004, 4745522, 857840, 105620, 9516, 644, 32, 1;
%e A135891 308478492, 262203558, 84534154, 15907004, 2052450, 196400, 14490, 832, 36, 1;
%e A135891 where P = A135880 begins:
%e A135891 1;
%e A135891 1, 1;
%e A135891 2, 2, 1;
%e A135891 6, 7, 3, 1;
%e A135891 25, 34, 15, 4, 1;
%e A135891 138, 215, 99, 26, 5, 1;
%e A135891 970, 1698, 814, 216, 40, 6, 1; ...
%e A135891 and Q = P^2 = A135885 begins:
%e A135891 1;
%e A135891 2, 1;
%e A135891 6, 4, 1;
%e A135891 25, 20, 6, 1;
%e A135891 138, 126, 42, 8, 1;
%e A135891 970, 980, 351, 72, 10, 1;
%e A135891 8390, 9186, 3470, 748, 110, 12, 1; ...
%e A135891 where column k of Q equals column 0 of Q^(k+1) for k>=0
%e A135891 and column 0 of Q equals column 0 of P shift left.
%o A135891 (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^4)[n+1,k+1]}
%Y A135891 Cf. A135886 (column 0); A135880 (P), A135885 (Q=P^2), A135893 (Q^3).
%K A135891 nonn,tabl
%O A135891 0,2
%A A135891 _Paul D. Hanna_, Dec 15 2007