OFFSET
0,5
COMMENTS
A(n,k) is the k-th binomial transform of A000312 evaluated at n.
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
N. J. A. Sloane, Transforms
FORMULA
E.g.f. of column k: exp(k*x)/(1 + LambertW(-x)).
A(n,k) = Sum_{j=0..n} binomial(n,j)*k^(n-j)*j^j. - Fabian Pereyra, Jul 16 2024
EXAMPLE
E.g.f. of column k: A_k(x) = 1 + (k + 1)*x/1! + (k^2 + 2*k + 4)*x^2/2! + (k^3 + 3*k^2 + 12*k + 27)*x^3/3! + (k^4 + 4*k^3 + 24*k^2 + 108*k + 256)*x^4/4! + ...
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, ...
4, 7, 12, 19, 28, 39, ...
27, 43, 71, 117, 187, 287, ...
256, 393, 616, 985, 1584, 2521, ...
3125, 4721, 7197, 11123, 17429, 27525, ...
MATHEMATICA
Table[Function[k, n!*SeriesCoefficient[Exp[k x]/(1 + LambertW[-x]), {x, 0, n}]][j - n], {j, 0, 10}, {n, 0, j}] // Flatten (* G. C. Greubel, Nov 09 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Aug 11 2017
STATUS
approved