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A355423
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(Sum_{j=1..k} (exp(j*x) - 1)).
2
1, 1, 0, 1, 1, 0, 1, 3, 2, 0, 1, 6, 14, 5, 0, 1, 10, 50, 81, 15, 0, 1, 15, 130, 504, 551, 52, 0, 1, 21, 280, 2000, 5870, 4266, 203, 0, 1, 28, 532, 6075, 35054, 76872, 36803, 877, 0, 1, 36, 924, 15435, 148429, 684000, 1111646, 348543, 4140, 0
OFFSET
0,8
FORMULA
T(0,k) = 1 and T(n,k) = Sum_{i=1..n} (Sum_{j=1..k} j^i) * binomial(n-1,i-1) * T(n-i,k) for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 3, 6, 10, 15, ...
0, 2, 14, 50, 130, 280, ...
0, 5, 81, 504, 2000, 6075, ...
0, 15, 551, 5870, 35054, 148429, ...
0, 52, 4266, 76872, 684000, 4004100, ...
CROSSREFS
Columns k=0-4 give: A000007, A000110, A355291, A355421, A355422.
Main diagonal gives A320288.
Sequence in context: A292717 A365727 A054654 * A345066 A253669 A154477
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jul 01 2022
STATUS
approved