A135891 Triangle, read by rows, equal to P^4, where triangle P = A135880; also equals Q^2, where triangle Q = P^2 = A135885.
1, 4, 1, 20, 8, 1, 126, 64, 12, 1, 980, 580, 132, 16, 1, 9186, 6064, 1554, 224, 20, 1, 101492, 72832, 20260, 3240, 340, 24, 1, 1296934, 995050, 294218, 50496, 5830, 480, 28, 1, 18868652, 15301004, 4745522, 857840, 105620, 9516, 644, 32, 1, 308478492
Offset: 0
Examples
Triangle P^4 = Q^2 begins: 1; 4, 1; 20, 8, 1; 126, 64, 12, 1; 980, 580, 132, 16, 1; 9186, 6064, 1554, 224, 20, 1; 101492, 72832, 20260, 3240, 340, 24, 1; 1296934, 995050, 294218, 50496, 5830, 480, 28, 1; 18868652, 15301004, 4745522, 857840, 105620, 9516, 644, 32, 1; 308478492, 262203558, 84534154, 15907004, 2052450, 196400, 14490, 832, 36, 1; where P = A135880 begins: 1; 1, 1; 2, 2, 1; 6, 7, 3, 1; 25, 34, 15, 4, 1; 138, 215, 99, 26, 5, 1; 970, 1698, 814, 216, 40, 6, 1; ... and Q = P^2 = 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) for k>=0 and column 0 of Q equals column 0 of P shift left.
Programs
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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]}