A381601
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x)^3 * A(x*A(x)^3)^3).
Original entry on oeis.org
1, 1, 7, 79, 1134, 18953, 353134, 7154751, 155181240, 3565276582, 86122663681, 2175366732971, 57218428637862, 1562164759518688, 44156180231275177, 1289514761824080659, 38840440076269957435, 1204858168452465020445, 38445264045516464373511
Offset: 0
-
a(n, k=1) = 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)));
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)));
A381595
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x) * A(x*A(x)))^3.
Original entry on oeis.org
1, 3, 24, 280, 4044, 67365, 1246534, 25051422, 538836147, 12279937669, 294374405652, 7382843258466, 192917842671564, 5235276617405133, 147163222059602313, 4275948043251399950, 128196303568520249238, 3959890522003241945409, 125863828745364900374059
Offset: 0
-
a(n, k=3) = 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)));
A381648
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 A381649.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 11, 44, 0, 1, 4, 18, 98, 510, 0, 1, 5, 26, 163, 1133, 7024, 0, 1, 6, 35, 240, 1884, 15508, 109362, 0, 1, 7, 45, 330, 2779, 25659, 239808, 1871530, 0, 1, 8, 56, 434, 3835, 37704, 394313, 4076904, 34590180, 0, 1, 9, 68, 553, 5070, 51891, 576178, 6661602, 74895252, 682396379, 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, 44, 98, 163, 240, 330, 434, ...
0, 510, 1133, 1884, 2779, 3835, 5070, ...
0, 7024, 15508, 25659, 37704, 51891, 68490, ...
0, 109362, 239808, 394313, 576178, 789055, 1036973, ...
-
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)));
Showing 1-4 of 4 results.