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A355427
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 - Sum_{j=1..k} (exp(j*x) - 1)/j).
3
1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 11, 13, 0, 1, 4, 24, 89, 75, 0, 1, 5, 42, 284, 959, 541, 0, 1, 6, 65, 654, 4476, 12917, 4683, 0, 1, 7, 93, 1255, 13564, 88178, 208781, 47293, 0, 1, 8, 126, 2143, 32275, 351634, 2084564, 3937019, 545835, 0
OFFSET
0,8
FORMULA
T(0,k) = 1 and T(n,k) = Sum_{i=1..n} (Sum_{j=1..k} j^(i-1)) * binomial(n,i) * T(n-i,k) for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 3, 11, 24, 42, 65, ...
0, 13, 89, 284, 654, 1255, ...
0, 75, 959, 4476, 13564, 32275, ...
0, 541, 12917, 88178, 351634, 1037479, ...
CROSSREFS
Columns k=0..3 give A000007, A000670, A355425, A355426.
Main diagonal gives A355428.
Sequence in context: A349971 A340986 A340798 * A122078 A292783 A320354
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jul 01 2022
STATUS
approved