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)));
A384145
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x*A(x)^3) ).
Original entry on oeis.org
1, 1, 2, 8, 44, 298, 2359, 21112, 209175, 2262121, 26431042, 331096188, 4419824468, 62565545535, 935341395343, 14716294925179, 242945752432294, 4197094127399756, 75698807290515322, 1422350601250404765, 27788515730656558613, 563512508612712699574, 11841983002490204813514
Offset: 0
-
a(n, k=1) = 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)));
A384649
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x*A(x)^4) ).
Original entry on oeis.org
1, 1, 2, 9, 56, 432, 3935, 40820, 471633, 5980210, 82329140, 1220547845, 19359684220, 326799737576, 5844913732057, 110341722975077, 2191461358459051, 45656013573862832, 995196646595460516, 22644288881875546322, 536706817952488705651, 13225669497771610891404
Offset: 0
-
a(n, k=1) = 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)));
Showing 1-4 of 4 results.