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URL: https://oeis.org/A157393

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A157393
A partition product of Stirling_1 type [parameter k = 3] with biggest-part statistic (triangle read by rows).
11
1, 1, 3, 1, 9, 6, 1, 45, 24, 6, 1, 165, 240, 30, 0, 1, 855, 1560, 360, 0, 0, 1, 3843, 12180, 3360, 0, 0, 0, 1, 21819, 96096, 30660, 0, 0, 0, 0, 1, 114075, 794304, 318276, 0, 0, 0, 0, 0, 1, 703215, 6850080, 3270960, 0, 0, 0, 0, 0, 0, 1, 4125495, 62516520, 35053920, 0, 0
OFFSET
1,3
COMMENTS
Partition product prod_{j=0..n-2}(k-n+j+2) and n! at k = 3, summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A144877.
Same partition product with length statistic is A049410.
Diagonal a(A000217(n)) = falling_factorial(3,n-1), row in A008279.
Row sum is A049426.
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+5).
KEYWORD
easy,nonn,tabl
AUTHOR
Peter Luschny, Mar 07 2009, Mar 14 2009
STATUS
approved