A381572
G.f. A(x) satisfies A(x) = 1/(1 - x*A(x*A(x)))^2.
Original entry on oeis.org
1, 2, 7, 38, 267, 2232, 21200, 222556, 2536661, 31010886, 403097573, 5535291884, 79900803514, 1207657432714, 19052200105025, 312909670649562, 5338325737985841, 94422672774323512, 1728653714036740230, 32708138881741705812, 638762549199936808759, 12859693257887577375744
Offset: 0
-
a(n, k=1) = if(k==0, 0^n, 2*k*sum(j=0, n, binomial(2*n-j+2*k, j)/(2*n-j+2*k)*a(n-j, j)));
A381573
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A381574.
Original entry on oeis.org
1, 1, 0, 1, 3, 0, 1, 6, 15, 0, 1, 9, 39, 118, 0, 1, 12, 72, 326, 1206, 0, 1, 15, 114, 651, 3345, 14712, 0, 1, 18, 165, 1120, 6822, 40200, 204385, 0, 1, 21, 225, 1760, 12123, 81675, 547146, 3143826, 0, 1, 24, 294, 2598, 19815, 145968, 1096080, 8239938, 52580328, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 3, 6, 9, 12, 15, ...
0, 15, 39, 72, 114, 165, ...
0, 118, 326, 651, 1120, 1760, ...
0, 1206, 3345, 6822, 12123, 19815, ...
0, 14712, 40200, 81675, 145968, 241773, ...
-
a(n, k) = if(k==0, 0^n, 3*k*sum(j=0, n, binomial(3*n-2*j+3*k, j)/(3*n-2*j+3*k)*a(n-j, j)));
A381592
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of B(x)^k, where B(x) is the g.f. of A381600.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 11, 39, 0, 1, 4, 18, 88, 383, 0, 1, 5, 26, 148, 869, 4360, 0, 1, 6, 35, 220, 1473, 9876, 55201, 0, 1, 7, 45, 305, 2211, 16740, 124473, 758877, 0, 1, 8, 56, 404, 3100, 25164, 210260, 1701630, 11157081, 0, 1, 9, 68, 518, 4158, 35381, 315312, 2860317, 24870695, 173623407, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 5, 11, 18, 26, 35, 45, ...
0, 39, 88, 148, 220, 305, 404, ...
0, 383, 869, 1473, 2211, 3100, 4158, ...
0, 4360, 9876, 16740, 25164, 35381, 47646, ...
0, 55201, 124473, 210260, 315312, 442710, 595892, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n+j+k, j)/(2*n+j+k)*a(n-j, 2*j)));
Showing 1-3 of 3 results.