A381574
G.f. A(x) satisfies A(x) = 1/(1 - x*A(x*A(x)))^3.
Original entry on oeis.org
1, 3, 15, 118, 1206, 14712, 204385, 3143826, 52580328, 944416084, 18056415144, 365065244238, 7765839784508, 173123253590079, 4031536347783786, 97807655876704029, 2466489368705170539, 64527021089110890192, 1748298996924574135699, 48982266056400514509660
Offset: 0
-
a(n, k=1) = 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)));
A381594
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 A381601.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 15, 79, 0, 1, 4, 24, 172, 1134, 0, 1, 5, 34, 280, 2475, 18953, 0, 1, 6, 45, 404, 4044, 41280, 353134, 0, 1, 7, 57, 545, 5863, 67365, 766291, 7154751, 0, 1, 8, 70, 704, 7955, 97620, 1246534, 15460284, 155181240, 0, 1, 9, 84, 882, 10344, 132486, 1801536, 25051422, 333896388, 3565276582, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 7, 15, 24, 34, 45, 57, ...
0, 79, 172, 280, 404, 545, 704, ...
0, 1134, 2475, 4044, 5863, 7955, 10344, ...
0, 18953, 41280, 67365, 97620, 132486, 172434, ...
0, 353134, 766291, 1246534, 1801536, 2439615, 3169770, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n+j+k, j)/(3*n+j+k)*a(n-j, 3*j)));
A381571
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 A381572.
Original entry on oeis.org
1, 1, 0, 1, 2, 0, 1, 4, 7, 0, 1, 6, 18, 38, 0, 1, 8, 33, 104, 267, 0, 1, 10, 52, 206, 735, 2232, 0, 1, 12, 75, 352, 1488, 6064, 21200, 0, 1, 14, 102, 550, 2626, 12246, 56510, 222556, 0, 1, 16, 133, 808, 4265, 21752, 112669, 581452, 2536661, 0, 1, 18, 168, 1134, 6537, 35812, 198808, 1140150, 6501267, 31010886, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 2, 4, 6, 8, 10, 12, ...
0, 7, 18, 33, 52, 75, 102, ...
0, 38, 104, 206, 352, 550, 808, ...
0, 267, 735, 1488, 2626, 4265, 6537, ...
0, 2232, 6064, 12246, 21752, 35812, 55944, ...
0, 21200, 56510, 112669, 198808, 327010, 512934, ...
-
a(n, k) = 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)));
Showing 1-3 of 3 results.