A157392 - OEIS

A157392

A partition product of Stirling_1 type [parameter k = 2] with biggest-part statistic (triangle read by rows).

1, 1, 2, 1, 6, 2, 1, 24, 8, 0, 1, 80, 60, 0, 0, 1, 330, 320, 0, 0, 0, 1, 1302, 2030, 0, 0, 0, 0, 1, 5936, 12432, 0, 0, 0, 0, 0, 1, 26784, 81368, 0, 0, 0, 0, 0, 0, 1, 133650, 545120, 0, 0, 0, 0, 0, 0, 0, 1, 669350, 3825690

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OFFSET

1,3

COMMENTS

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

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

Underlying partition triangle is A144358.

Same partition product with length statistic is A049404.

Diagonal a(A000217(n)) = falling_factorial(2,n-1), row in A008279

Row sum is A049425.

LINKS

Table of n, a(n) for n=1..58.

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+4).

CROSSREFS

Cf. A157386, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395

Sequence in context: A179863 A069123 A134133 * A321352 A134134 A222005

Adjacent sequences: A157389 A157390 A157391 * A157393 A157394 A157395

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Luschny, Mar 07 2009, Mar 14 2009

STATUS

approved