A379599
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 A088714.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 7, 13, 0, 1, 4, 12, 32, 69, 0, 1, 5, 18, 58, 173, 419, 0, 1, 6, 25, 92, 321, 1054, 2809, 0, 1, 7, 33, 135, 523, 1971, 7039, 20353, 0, 1, 8, 42, 188, 790, 3248, 13158, 50632, 157199, 0, 1, 9, 52, 252, 1134, 4976, 21740, 94194, 387613, 1281993, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 3, 7, 12, 18, 25, 33, ...
0, 13, 32, 58, 92, 135, 188, ...
0, 69, 173, 321, 523, 790, 1134, ...
0, 419, 1054, 1971, 3248, 4976, 7260, ...
0, 2809, 7039, 13158, 21740, 33480, 49210, ...
-
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)));
A380178
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 A162659.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 8, 22, 0, 1, 4, 15, 62, 281, 0, 1, 5, 24, 126, 792, 5396, 0, 1, 6, 35, 220, 1641, 14922, 142297, 0, 1, 7, 48, 350, 2960, 30708, 384316, 4865806, 0, 1, 8, 63, 522, 4905, 55604, 777537, 12836406, 207407489, 0, 1, 9, 80, 742, 7656, 93300, 1393720, 25450806, 535396784, 10710044776, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 3, 8, 15, 24, 35, 48, ...
0, 22, 62, 126, 220, 350, 522, ...
0, 281, 792, 1641, 2960, 4905, 7656, ...
0, 5396, 14922, 30708, 55604, 93300, 148446, ...
0, 142297, 384316, 777537, 1393720, 2330305, 3716532, ...
-
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)));
A384761
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 A384760.
Original entry on oeis.org
1, 1, 0, 1, -1, 0, 1, -2, 1, 0, 1, -3, 4, 5, 0, 1, -4, 9, 4, -35, 0, 1, -5, 16, -9, -104, -281, 0, 1, -6, 25, -40, -171, -112, 5671, 0, 1, -7, 36, -95, -176, 717, 14164, 42671, 0, 1, -8, 49, -180, -35, 2176, 20619, -18104, -2179127, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, -1, -2, -3, -4, -5, ...
0, 1, 4, 9, 16, 25, ...
0, 5, 4, -9, -40, -95, ...
0, -35, -104, -171, -176, -35, ...
0, -281, -112, 717, 2176, 3875, ...
-
a(n, k) = if(k==0, 0^n, (-1)^n*k*sum(j=0, n, (n+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)));
A384788
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 A384787.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 16, 148, 0, 1, 4, 27, 338, 7381, 0, 1, 5, 40, 576, 16240, 801536, 0, 1, 6, 55, 868, 26829, 1697602, 186678019, 0, 1, 7, 72, 1220, 39424, 2701488, 384962560, 93865986880, 0, 1, 8, 91, 1638, 54325, 3828164, 595921743, 190657584770, 102755888482153, 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, 148, 338, 576, 868, 1220, ...
0, 7381, 16240, 26829, 39424, 54325, ...
0, 801536, 1697602, 2701488, 3828164, 5094400, ...
-
a(n, k) = if(k==0, 0^n, k*sum(j=0, n, 2^(n-j)*(n+k)^(j-1)*binomial(n, j)*a(n-j, j)));
Showing 1-5 of 5 results.