

A118984


Triangular T(n,k) which contains in column k >= 0 the elements of the Stirling transform of the unsigned sequence Stirling1(j+k,j), j >= 0.


1



1, 2, 1, 5, 6, 2, 15, 31, 23, 6, 52, 160, 195, 110, 24, 203, 856, 1505, 1365, 634, 120, 877, 4802, 11312, 14560, 10738, 4284, 720, 4140, 28337, 85225, 145096, 150325, 94444, 33228, 5040, 21147, 175896, 652703, 1404186, 1908249, 1672524, 921212, 291024
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OFFSET

1,2


COMMENTS

The initial array of unsigned Stirling numbers of the first kind (filled with an appropriate number of zeros) starts (see A094638)
1, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 0, 0, 0, 0, 0, 0, ...
1, 3, 2, 0, 0, 0, 0, 0, ...
1, 6, 11, 6, 0, 0, 0, 0, ...
1, 10, 35, 50, 24, 0, 0, 0, ...
1, 15, 85, 225, 274, 120, 0, 0, ...
1, 21, 175, 735, 1624, 1764, 720, 0, ...
1, 28, 322, 1960, 6769, 13132, 13068, 5040, ...
The Stirling transform is then applied on each individual column.  R. J. Mathar, May 19 2016.


LINKS



EXAMPLE

The array begins
1;
2, 1;
5, 6, 2;
15, 31, 23, 6;
52, 160, 195, 110, 24;
203, 856, 1505, 1365, 634, 120;
877, 4802, 11312, 14560, 10738, 4284, 720;
4140, 28337, 85225, 145096, 150325, 94444, 33228, 5040;


MAPLE

read("transforms"):
[seq(0, j=0..k2), seq( (1)^k*combinat[stirling1](j+k, j), j=0..n)] ;
STIRLING(%) ;
op(n, %) ;


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



