

A157403


A partition product of Stirling_2 type [parameter k = 3] with biggestpart statistic (triangle read by rows).


10



1, 1, 3, 1, 9, 21, 1, 45, 84, 231, 1, 165, 840, 1155, 3465, 1, 855, 8610, 13860, 20790, 65835, 1, 3843, 64680, 250635, 291060, 460845, 1514205, 1, 21819, 689136, 3969735, 6015240, 7373520, 12113640, 40883535, 1, 114075
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Partition product of prod_{j=0..n1}((k + 1)*j  1) and n! at k = 3,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A143173.
Same partition product with length statistic is A000369.
Diagonal a(A000217) = A008545
Row sum is A016036.


LINKS

Table of n, a(n) for n=1..38.
Peter Luschny, Counting with Partitions.
Peter Luschny, Generalized Stirling_2 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..n1}(4*j  1).


CROSSREFS

Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157404, A157405
Sequence in context: A118793 A247231 A160568 * A225118 A273464 A105951
Adjacent sequences: A157400 A157401 A157402 * A157404 A157405 A157406


KEYWORD

easy,nonn,tabl


AUTHOR

Peter Luschny, Mar 09 2009


STATUS

approved



