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)));
A381570
G.f. A(x) satisfies A(x) = (1 + x*A(x*A(x)))^3.
Original entry on oeis.org
1, 3, 12, 82, 732, 7944, 99156, 1381464, 21065853, 346932822, 6112226961, 114383442888, 2261347164766, 47025363829497, 1025005545866361, 23349137897005296, 554467427766694440, 13696046757037152183, 351231525904387758222, 9335221780768641038952
Offset: 0
-
a(n, k=1) = 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)));
A381567
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 A381568.
Original entry on oeis.org
1, 1, 0, 1, 2, 0, 1, 4, 5, 0, 1, 6, 14, 22, 0, 1, 8, 27, 64, 126, 0, 1, 10, 44, 134, 365, 884, 0, 1, 12, 65, 240, 777, 2492, 7149, 0, 1, 14, 90, 390, 1438, 5238, 19578, 64688, 0, 1, 16, 119, 592, 2440, 9696, 40244, 172356, 641836, 0, 1, 18, 152, 854, 3891, 16632, 73408, 345726, 1668686, 6888740, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 2, 4, 6, 8, 10, 12, ...
0, 5, 14, 27, 44, 65, 90, ...
0, 22, 64, 134, 240, 390, 592, ...
0, 126, 365, 777, 1438, 2440, 3891, ...
0, 884, 2492, 5238, 9696, 16632, 27036, ...
0, 7149, 19578, 40244, 73408, 125035, 203258, ...
-
a(n, k) = 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)));
Showing 1-3 of 3 results.