Original entry on oeis.org
1, 1, 1, 3, 7, 36, 139, 1036, 5711, 56355, 408354, 5045370, 45605881, 679409158, 7390305396, 129195427716, 1647470410551, 33114233390505, 485292763088275, 11038606786054201, 183049273155939442, 4652371578279864792
Offset: 0
1 = 1*(1-x) + 1*x*(1-x) + 1*x^2*(1-x)(1-2x) + 3*x^3*(1-x)(1-2x)
+ 7*x^4*(1-x)(1-2x)(1-3x) + 36*x^5*(1-x)(1-2x)(1-3x)
+ 139*x^6*(1-x)(1-2x)(1-3x)(1-4x) + 1036*x^7*(1-x)(1-2x)(1-3x)(1-4x) + ...
+ A082162(n)*x^(2n)*(1-x)(1-2x)*..*(1-(n+1)x)
+ A102921(n)*x^(2n+1)*(1-x)(1-2x)*..*(1-(n+1)x) + ...
-
{a(n)=if(n==0,1,polcoeff(1-sum(k=0,n-1,a(k)*x^k*prod(j=1,k\2+1,1-j*x+x*O(x^n))),n))}
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
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) + ...
-
{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))}
Original entry on oeis.org
1, 3, 8, 24, 95, 472, 3010, 22508, 198157, 1969757, 22006039, 272436985, 3691859826, 54696947677, 872698586012, 15055534230363, 276756250035637, 5449734493500830, 113510195694700702, 2512765185249336397
Offset: 0
-
{T(n,k)=if(nA102916 */ {a(n)=sum(k=0,n,T(n,k))}
A102920
Triangular matrix, read by rows, equal to the matrix square of A102098.
Original entry on oeis.org
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
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],...
-
{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])}
Showing 1-4 of 4 results.
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