A384652
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 A384145.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 8, 0, 1, 4, 9, 20, 44, 0, 1, 5, 14, 37, 108, 298, 0, 1, 6, 20, 60, 198, 716, 2359, 0, 1, 7, 27, 90, 321, 1290, 5554, 21112, 0, 1, 8, 35, 128, 485, 2064, 9821, 48838, 209175, 0, 1, 9, 44, 175, 699, 3091, 15452, 84888, 476714, 2262121, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 2, 5, 9, 14, 20, 27, ...
0, 8, 20, 37, 60, 90, 128, ...
0, 44, 108, 198, 321, 485, 699, ...
0, 298, 716, 1290, 2064, 3091, 4434, ...
0, 2359, 5554, 9821, 15452, 22805, 32315, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-2*j+k, j)/(3*n-2*j+k)*a(n-j, j)));
A384653
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 A384649.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 9, 0, 1, 4, 9, 22, 56, 0, 1, 5, 14, 40, 134, 432, 0, 1, 6, 20, 64, 240, 1012, 3935, 0, 1, 7, 27, 95, 381, 1779, 9039, 40820, 0, 1, 8, 35, 134, 565, 2780, 15596, 92246, 471633, 0, 1, 9, 44, 182, 801, 4071, 23950, 156597, 1051558, 5980210, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 2, 5, 9, 14, 20, 27, ...
0, 9, 22, 40, 64, 95, 134, ...
0, 56, 134, 240, 381, 565, 801, ...
0, 432, 1012, 1779, 2780, 4071, 5718, ...
0, 3935, 9039, 15596, 23950, 34515, 47786, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(4*n-3*j+k, j)/(4*n-3*j+k)*a(n-j, j)));
A384654
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 A384650.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 10, 0, 1, 4, 9, 24, 69, 0, 1, 5, 14, 43, 162, 592, 0, 1, 6, 20, 68, 285, 1362, 6052, 0, 1, 7, 27, 100, 445, 2352, 13664, 70870, 0, 1, 8, 35, 140, 650, 3612, 23171, 157592, 928497, 0, 1, 9, 44, 189, 909, 5201, 34972, 263190, 2039543, 13404514, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 2, 5, 9, 14, 20, 27, ...
0, 10, 24, 43, 68, 100, 140, ...
0, 69, 162, 285, 445, 650, 909, ...
0, 592, 1362, 2352, 3612, 5201, 7188, ...
0, 6052, 13664, 23171, 34972 ,49540, 67433, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(5*n-4*j+k, j)/(5*n-4*j+k)*a(n-j, j)));
Showing 1-3 of 3 results.