A381566
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 A087949.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 3, 2, 0, 1, 4, 6, 6, 5, 0, 1, 5, 10, 13, 15, 16, 0, 1, 6, 15, 24, 33, 46, 59, 0, 1, 7, 21, 40, 63, 99, 164, 246, 0, 1, 8, 28, 62, 110, 188, 343, 662, 1131, 0, 1, 9, 36, 91, 180, 331, 638, 1344, 2961, 5655, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 1, 3, 6, 10, 15, 21, ...
0, 2, 6, 13, 24, 40, 62, ...
0, 5, 15, 33, 63, 110, 180, ...
0, 16, 46, 99, 188, 331, 552, ...
0, 59, 164, 343, 638, 1110, 1845, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(n-j+k, j)/(n-j+k)*a(n-j, j)));
A381568
G.f. A(x) satisfies A(x) = (1 + x*A(x*A(x)))^2.
Original entry on oeis.org
1, 2, 5, 22, 126, 884, 7149, 64688, 641836, 6888740, 79203860, 968503090, 12525131474, 170555767116, 2436592516874, 36409825487380, 567612675812796, 9211031425896752, 155283809480528788, 2714788300934206360, 49140787009610861896, 919625415852055598804, 17768937720619971300781
Offset: 0
-
a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n-2*j+2*k, j)/(n-j+k)*a(n-j, j)));
A381569
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 A381570.
Original entry on oeis.org
1, 1, 0, 1, 3, 0, 1, 6, 12, 0, 1, 9, 33, 82, 0, 1, 12, 63, 236, 732, 0, 1, 15, 102, 489, 2100, 7944, 0, 1, 18, 150, 868, 4428, 22248, 99156, 0, 1, 21, 207, 1400, 8121, 46422, 270268, 1381464, 0, 1, 24, 273, 2112, 13665, 85272, 552540, 3668568, 21065853, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 3, 6, 9, 12, 15, ...
0, 12, 33, 63, 102, 150, ...
0, 82, 236, 489, 868, 1400, ...
0, 732, 2100, 4428, 8121, 13665, ...
0, 7944, 22248, 46422, 85272, 145143, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-3*j+3*k, j)/(n-j+k)*a(n-j, j)));
Showing 1-3 of 3 results.