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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 (list; table; graph; refs; listen; history; text; internal format)
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
Sela Fried, The expected degree of noninvertibility of compositions of functions and a related combinatorial identity, arXiv:2202.13061 [math.CO], 2022. See Corollary 2.6 for a combinatorial identity of a signed version of this sequence.
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"):
A118984 := proc(n, k)
[seq(0, j=0..k-2), seq( (-1)^k*combinat[stirling1](j+k, j), j=0..n)] ;
STIRLING(%) ;
op(n, %) ;
end proc: # R. J. Mathar, May 19 2016
CROSSREFS
Cf. A000110 (first column), A000142 (diagonal), A000670 (row sums), A003128 (2nd column), A008275, A008277.
Sequence in context: A062991 A234950 A275228 * A073474 A067311 A341487
KEYWORD
nonn,tabl
AUTHOR
Alford Arnold, May 07 2006
EXTENSIONS
Edited by R. J. Mathar, May 19 2016
STATUS
approved

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Last modified June 14 01:54 EDT 2024. Contains 373391 sequences. (Running on oeis4.)