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A091039 Triangle of scaled second column sequences of (k,k)-Stirling2 arrays. 3
1, 3, 1, 7, 8, 1, 15, 52, 30, 1, 31, 320, 756, 144, 1, 63, 1936, 18360, 17856, 840, 1, 127, 11648, 441936, 2156544, 619200, 5760, 1, 255, 69952, 10614240, 259117056, 447552000, 29548800, 45360, 1, 511, 419840, 254788416, 31102009344 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n-1,k)= S2_{k,k}(n,k+1)/(k*k!), n>=2, 1<=k<= n-1, with S2_{k,k} the r=k,s=k Stirling2 array S_{k,k} of the Blasiak et al. reference.

REFERENCES

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.

M. Schork, On the combinatorics of normal ordering bosonic operators and deforming it, J. Phys. A 36 (2003) 4651-4665.

LINKS

Table of n, a(n) for n=1..40.

W. Lang, First 9 rows.

FORMULA

a(n, k)=(k!^(n-k+1))*((k+1)^(n-k+1)-1)/(k*k!) if n >= k >= 1, else 0.

G.f. column k (without leading zeros): 1/((1-(k+1)!*x)*(1-k!*x)) = (1/(1-(k+1)!*x) - 1/(1-k!*x))/(k*k!*x).

EXAMPLE

[1];[3,1];[7,8,1];[15,52,30,1];...

CROSSREFS

Cf. A091040 (row sums), A091041 (alternating row sums).

Sequence in context: A058606 A135284 A016647 * A217594 A340616 A120472

Adjacent sequences:  A091036 A091037 A091038 * A091040 A091041 A091042

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Jan 23 2004

STATUS

approved

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Last modified July 5 14:18 EDT 2022. Contains 355099 sequences. (Running on oeis4.)