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A292717
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. -log(1 - x)/(1 - x)^k.
0
0, 0, 1, 0, 1, 1, 0, 1, 3, 2, 0, 1, 5, 11, 6, 0, 1, 7, 26, 50, 24, 0, 1, 9, 47, 154, 274, 120, 0, 1, 11, 74, 342, 1044, 1764, 720, 0, 1, 13, 107, 638, 2754, 8028, 13068, 5040, 0, 1, 15, 146, 1066, 5944, 24552, 69264, 109584, 40320, 0, 1, 17, 191, 1650, 11274, 60216, 241128, 663696, 1026576, 362880
OFFSET
0,9
FORMULA
E.g.f. of column k: -log(1 - x)/(1 - x)^k.
EXAMPLE
E.g.f. of column k: A_k(x) = x/1! + (2*k + 1)*x^2/2! + (3*k^2 + 6*k + 2)*x^3/3! + 2*(2*k^3 + 9*k^2 + 11*k + 3)*x^4/4! + ...
Square array begins:
0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, ...
1, 3, 5, 7, 9, 11, ...
2, 11, 26, 47, 74, 107, ...
6, 50, 154, 342, 638, 1066, ...
24, 274, 1044, 2754, 5944, 11274, ...
MATHEMATICA
Table[Function[k, n! SeriesCoefficient[-Log[1 - x]/(1 - x)^k, {x, 0, n}]][j - n], {j, 0, 10}, {n, 0, j}] // Flatten
CROSSREFS
Columns k=0..11 give A104150, A000254, A001705, A001711 (with offset 1), A001716 (with offset 1), A001721 (with offset 1), A051524, A051545, A051560, A051562, A051564, A203147.
Rows n=0..3 give A000004, A000012, A005408, A080663 (with offset 0).
Main diagonal gives A058806.
Sequence in context: A373451 A081576 A330785 * A365727 A054654 A355423
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Sep 21 2017
STATUS
approved