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)));
A384650
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x*A(x)^5) ).
Original entry on oeis.org
1, 1, 2, 10, 69, 592, 6052, 70870, 928497, 13404514, 210892157, 3584892350, 65390514877, 1272723903336, 26307949481077, 575201364472316, 13255835789428863, 320999903683710948, 8145524458876305526, 216062918679078474529, 5977572987203090333399
Offset: 0
-
a(n, k=1) = 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)));
A384651
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 A162661.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 7, 0, 1, 4, 9, 18, 33, 0, 1, 5, 14, 34, 84, 189, 0, 1, 6, 20, 56, 159, 472, 1249, 0, 1, 7, 27, 85, 265, 882, 3057, 9237, 0, 1, 8, 35, 122, 410, 1460, 5615, 22190, 74972, 0, 1, 9, 44, 168, 603, 2256, 9166, 40053, 177149, 659042, 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, 7, 18, 34, 56, 85, 122, ...
0, 33, 84, 159, 265, 410, 603, ...
0, 189, 472, 882, 1460, 2256, 3330, ...
0, 1249, 3057, 5615, 9166, 14015, 20540, ...
-
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, j)));
Showing 1-4 of 4 results.