A102922 -id:A102922 - cp's OEIS frontend

A102920 Triangular matrix, read by rows, equal to the matrix square of A102098.

1, 3, 4, 36, 40, 9, 1036, 1128, 189, 16, 56355, 61120, 9720, 576, 25, 5045370, 5466320, 857466, 47040, 1375, 36, 679409158, 735847800, 114915375, 6155008, 163500, 2808, 49, 129195427716, 139910204080, 21813099606, 1158059520, 29767000, 458136

Offset: 0

Paul D. Hanna, Jan 21 2005

Column 0 is A102921. Column 1 is A102922.

			Rows begin:
[1],
[3,4],
[36,40,9],
[1036,1128,189,16],
[56355,61120,9720,576,25],
[5045370,5466320,857466,47040,1375,36],
[679409158,735847800,114915375,6155008,163500,2808,49],...

Cf. A102098, A102921, A102922, A102916.

{T(n,k)=local(A=matrix(1,1),B);A[1,1]=1; for (m=2,n+1,B=matrix(m,m);for (i=1,m, for (j=1,i, if(j==i,B[i,j]=j,B[i,j]=(A^3)[i-1,j]);));A=B); return((A^2)[n+1,k+1])}

A102918 Column 1 of triangle A102916.

Original entry on oeis.org

0, 2, 4, 8, 40, 152, 1128, 6200, 61120, 442552, 5466320, 49399320, 735847800, 8003532512, 139910204080, 1784040237288, 35858685086352, 525504809786112, 11953187179149408, 198213959637435608, 5037776918810353960

Offset: 0

Paul D. Hanna, Jan 21 2005

nonn

Also equals the interleaving of A102099 with A102922, which equal column 1 of triangle A102098 and its matrix square (A102920), respectively.

			2 = 2*(1-2x) + 4*x*(1-2x) + 8*x^2*(1-2x)(1-3x) + 40*x^3*(1-2x)(1-3x)
+ 152*x^4*(1-2x)(1-3x)(1-4x) + 1128*x^5*(1-2x)(1-3x)(1-4x)
+ 6200*x^6*(1-2x)(1-3x)(1-4x)(1-5x) + 61120*x^7*(1-2x)(1-3x)(1-4x)(1-5x) +...
+ A102099(n+1)*x^(2n)*(1-2x)(1-3x)*..*(1-(n+2)x)
+ A102922(n+1)*x^(2n+1)*(1-x)(1-2x)*..*(1-(n+2)x) + ...

Cf. A102916, A102099, A102922, A102098, A102920.

{a(n)=if(n==0,2,polcoeff(2-sum(k=0,n-1,a(k)*x^k*prod(j=2,k\2+2,1-j*x+x*O(x^n))),n))}

G.f.: 2 = Sum_{n>=0}(a(2*n+1)+a(2*n+2)*x)*x^(2*n)*Product_{k=2..n+2}(1-k*x) where a(2*n+1)=A102099(n+1) and a(2*n+2)=A102922(n+1) with a(0)=0.

cp's OEIS Frontend

A102920 Triangular matrix, read by rows, equal to the matrix square of A102098.

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