A384623
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 A384622.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 7, 0, 1, 3, 15, 75, 0, 1, 4, 24, 164, 989, 0, 1, 5, 34, 268, 2177, 14822, 0, 1, 6, 45, 388, 3585, 32672, 242833, 0, 1, 7, 57, 525, 5235, 53922, 534781, 4253818, 0, 1, 8, 70, 680, 7150, 78972, 882304, 9349160, 78573475, 0, 1, 9, 84, 854, 9354, 108251, 1292456, 15399930, 172255669, 1516124048, 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, 75, 164, 268, 388, 525, 680, ...
0, 989, 2177, 3585, 5235, 7150, 9354, ...
0, 14822, 32672, 53922, 78972, 108251, 142218, ...
0, 242833, 534781, 882304, 1292456, 1772920, 2332044, ...
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a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(n+j+k, j)/(n+j+k)*a(n-j, 5*j)));
A384619
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of (B(x)/x)^k, where B(x) is the g.f. of A213591.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 4, 0, 1, 3, 9, 24, 0, 1, 4, 15, 56, 178, 0, 1, 5, 22, 97, 420, 1512, 0, 1, 6, 30, 148, 738, 3572, 14152, 0, 1, 7, 39, 210, 1145, 6300, 33328, 142705, 0, 1, 8, 49, 284, 1655, 9832, 58702, 334354, 1528212, 0, 1, 9, 60, 371, 2283, 14321, 91640, 586635, 3559310, 17211564, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 4, 9, 15, 22, 30, 39, ...
0, 24, 56, 97, 148, 210, 284, ...
0, 178, 420, 738, 1145, 1655, 2283, ...
0, 1512, 3572, 6300, 9832, 14321, 19938, ...
0, 14152, 33328, 58702, 91640, 133720, 186753, ...
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a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(n+j+k, j)/(n+j+k)*a(n-j, 2*j)));
A384620
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of (B(x)/x)^k, where B(x) is the g.f. of A213639.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 11, 38, 0, 1, 4, 18, 86, 357, 0, 1, 5, 26, 145, 815, 3832, 0, 1, 6, 35, 216, 1389, 8758, 45189, 0, 1, 7, 45, 300, 2095, 14967, 103056, 572378, 0, 1, 8, 56, 398, 2950, 22668, 175937, 1300586, 7676653, 0, 1, 9, 68, 511, 3972, 32091, 266470, 2214012, 17368633, 107971691, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, 6, ...
0, 5, 11, 18, 26, 35, 45, ...
0, 38, 86, 145, 216, 300, 398, ...
0, 357, 815, 1389, 2095, 2950, 3972, ...
0, 3832, 8758, 14967, 22668, 32091, 43488, ...
0, 45189, 103056, 175937, 266470, 377620, 512705, ...
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a(n, k) = if(k==0, 0^n, k*sum(j=0, n, binomial(n+j+k, j)/(n+j+k)*a(n-j, 3*j)));
Showing 1-3 of 3 results.