A381594
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 A381601.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 15, 79, 0, 1, 4, 24, 172, 1134, 0, 1, 5, 34, 280, 2475, 18953, 0, 1, 6, 45, 404, 4044, 41280, 353134, 0, 1, 7, 57, 545, 5863, 67365, 766291, 7154751, 0, 1, 8, 70, 704, 7955, 97620, 1246534, 15460284, 155181240, 0, 1, 9, 84, 882, 10344, 132486, 1801536, 25051422, 333896388, 3565276582, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 7, 15, 24, 34, 45, 57, ...
0, 79, 172, 280, 404, 545, 704, ...
0, 1134, 2475, 4044, 5863, 7955, 10344, ...
0, 18953, 41280, 67365, 97620, 132486, 172434, ...
0, 353134, 766291, 1246534, 1801536, 2439615, 3169770, ...
-
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)));
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)));
A381649
G.f. A(x) satisfies A(x) = 1 + x * A(x)^2 * A(x*A(x)^3)^3.
Original entry on oeis.org
1, 1, 5, 44, 510, 7024, 109362, 1871530, 34590180, 682396379, 14251399805, 313170119013, 7207845252630, 173129413258492, 4327373963163746, 112289379643018983, 3018922654575996866, 83951253980821314446, 2411137697712963195801, 71427857356498491780290
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)));
Showing 1-4 of 4 results.