A381573
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 A381574.
Original entry on oeis.org
1, 1, 0, 1, 3, 0, 1, 6, 15, 0, 1, 9, 39, 118, 0, 1, 12, 72, 326, 1206, 0, 1, 15, 114, 651, 3345, 14712, 0, 1, 18, 165, 1120, 6822, 40200, 204385, 0, 1, 21, 225, 1760, 12123, 81675, 547146, 3143826, 0, 1, 24, 294, 2598, 19815, 145968, 1096080, 8239938, 52580328, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 3, 6, 9, 12, 15, ...
0, 15, 39, 72, 114, 165, ...
0, 118, 326, 651, 1120, 1760, ...
0, 1206, 3345, 6822, 12123, 19815, ...
0, 14712, 40200, 81675, 145968, 241773, ...
-
a(n, k) = if(k==0, 0^n, 3*k*sum(j=0, n, binomial(3*n-2*j+3*k, j)/(3*n-2*j+3*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)));
A381615
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x*A(x)^3)^3).
Original entry on oeis.org
1, 1, 4, 31, 320, 3969, 56080, 876204, 14860614, 270231265, 5223002719, 106613106181, 2287120272173, 51367948203527, 1204141944566399, 29385603693050274, 744943334951904519, 19580887642660810193, 532781828387893449124, 14984377196395037979472
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, 3*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)));
Showing 1-4 of 4 results.