A379598
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 A110447.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 5, 6, 0, 1, 4, 9, 16, 23, 0, 1, 5, 14, 31, 62, 104, 0, 1, 6, 20, 52, 123, 278, 531, 0, 1, 7, 27, 80, 213, 552, 1398, 2982, 0, 1, 8, 35, 116, 340, 964, 2750, 7718, 18109, 0, 1, 9, 44, 161, 513, 1561, 4784, 14976, 46083, 117545, 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, 6, 16, 31, 52, 80, 116, ...
0, 23, 62, 123, 213, 340, 513, ...
0, 104, 278, 552, 964, 1561, 2400, ...
0, 531, 1398, 2750, 4784, 7755, 11987, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(n+k, j)/(n+k)*a(n-j, j)));
A379168
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A140049.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 12, 55, 0, 1, 4, 21, 140, 1005, 0, 1, 5, 32, 261, 2600, 26601, 0, 1, 6, 45, 424, 4965, 68752, 941863, 0, 1, 7, 60, 635, 8304, 132003, 2414188, 42372177, 0, 1, 8, 77, 900, 12845, 223104, 4617675, 107385896, 2336926665, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 5, 12, 21, 32, 45, 60, ...
0, 55, 140, 261, 424, 635, 900, ...
0, 1005, 2600, 4965, 8304, 12845, 18840, ...
0, 26601, 68752, 132003, 223104, 350125, 522576, ...
0, 941863, 2414188, 4617675, 7806424, 12296935, 18477828, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (n+k)^(j-1)*binomial(n, j)*a(n-j, j)));
A384721
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384719.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 12, 61, 0, 1, 4, 21, 152, 1281, 0, 1, 5, 32, 279, 3200, 39641, 0, 1, 6, 45, 448, 5937, 98192, 1655713, 0, 1, 7, 60, 665, 9696, 181563, 4053688, 88312869, 0, 1, 8, 77, 936, 14705, 296864, 7430265, 213600200, 5792082817, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 5, 12, 21, 32, 45, ...
0, 61, 152, 279, 448, 665, ...
0, 1281, 3200, 5937, 9696, 14705, ...
0, 39641, 98192, 181563, 296864, 452525, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, 2*j)));
A384722
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384720.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 16, 118, 0, 1, 4, 27, 278, 3385, 0, 1, 5, 40, 486, 8008, 141556, 0, 1, 6, 55, 748, 14121, 333482, 7918489, 0, 1, 7, 72, 1070, 22000, 587268, 18524980, 561302470, 0, 1, 8, 91, 1458, 31945, 916084, 32452353, 1303041350, 48589734337, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 7, 16, 27, 40, 55, ...
0, 118, 278, 486, 748, 1070, ...
0, 3385, 8008, 14121, 22000, 31945, ...
0, 141556, 333482, 587268, 916084, 1334900, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, 3*j)));
A384741
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384739.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 28, 0, 1, 4, 15, 74, 461, 0, 1, 5, 24, 144, 1200, 11776, 0, 1, 6, 35, 244, 2325, 29842, 421207, 0, 1, 7, 48, 380, 3968, 56688, 1040896, 19832128, 0, 1, 8, 63, 558, 6285, 95524, 1933227, 47948490, 1179482201, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 3, 8, 15, 24, 35, ...
0, 28, 74, 144, 244, 380, ...
0, 461, 1200, 2325, 3968, 6285, ...
0, 11776, 29842, 56688, 95524, 150400, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (2*n-2*j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
A384742
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384740.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 34, 0, 1, 4, 15, 86, 665, 0, 1, 5, 24, 162, 1656, 20556, 0, 1, 6, 35, 268, 3081, 49802, 901417, 0, 1, 7, 48, 410, 5072, 90588, 2132476, 52455250, 0, 1, 8, 63, 594, 7785, 146484, 3792177, 121703094, 3885229665, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 3, 8, 15, 24, 35, ...
0, 34, 86, 162, 268, 410, ...
0, 665, 1656, 3081, 5072, 7785, ...
0, 20556, 49802, 90588, 146484, 221900, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (3*n-3*j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
A384690
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384689.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 16, 106, 0, 1, 4, 27, 254, 2593, 0, 1, 5, 40, 450, 6328, 89796, 0, 1, 6, 55, 700, 11457, 220362, 4085029, 0, 1, 7, 72, 1010, 18256, 402468, 10016860, 232694806, 0, 1, 8, 91, 1386, 27025, 648564, 18326853, 568220102, 16053415249, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 7, 16, 27, 40, 55, ...
0, 106, 254, 450, 700, 1010, ...
0, 2593, 6328, 11457, 18256, 27025, ...
0, 89796, 220362, 402468, 648564, 972900, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, (n+j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
Showing 1-7 of 7 results.