login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A157385 A partition product of Stirling_1 type [parameter k = -5] with biggest-part statistic (triangle read by rows). 9
1, 1, 5, 1, 15, 30, 1, 105, 120, 210, 1, 425, 1800, 1050, 1680, 1, 3075, 18600, 18900, 10080, 15120, 1, 15855, 174300, 338100, 211680, 105840, 151200, 1, 123515, 2227680, 4865700, 4327680, 2540160, 1209600, 1663200, 1, 757755 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = -5,

summed over parts with equal biggest part (see the Luschny link).

Underlying partition triangle is A144355.

Same partition product with length statistic is A049353.

Diagonal a(A000217(n)) = rising_factorial(5,n-1), A001720(n+3).

Row sum is A049378.

LINKS

Table of n, a(n) for n=1..38.

Peter Luschny, Counting with Partitions.

Peter Luschny, Generalized Stirling_1 Triangles.

FORMULA

T(n,0) = [n = 0] (Iverson notation) and for n > 0 and 1 <= m <= n

T(n,m) = Sum_{a} M(a)|f^a| where a = a_1,..,a_n such that

1*a_1+2*a_2+...+n*a_n = n and max{a_i} = m, M(a) = n!/(a_1!*..*a_n!),

f^a = (f_1/1!)^a_1*..*(f_n/n!)^a_n and f_n = product_{j=0..n-2}(j-n-3).

CROSSREFS

Cf. A157386, A157384, A157383, A157400, A126074, A157391, A157392, A157393, A157394, A157395

Sequence in context: A185263 A264616 A157395 * A157397 A157405 A283434

Adjacent sequences:  A157382 A157383 A157384 * A157386 A157387 A157388

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Luschny, Mar 07 2009, Mar 14 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.