A157391 A partition product of Stirling_1 type [parameter k = 1] with biggest-part statistic (triangle read by rows).

1, 1, 1, 1, 3, 0, 1, 9, 0, 0, 1, 25, 0, 0, 0, 1, 75, 0, 0, 0, 0, 1, 231, 0, 0, 0, 0, 0, 1, 763, 0, 0, 0, 0, 0, 0, 1, 2619, 0, 0, 0, 0, 0, 0, 0, 1, 9495, 0, 0, 0, 0, 0, 0, 0, 0, 1, 35695, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 140151

Offset

1,5

Comments

Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = 1,

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

Underlying partition triangle is A144357.

Same partition product with length statistic is A049403.

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

Row sum is A000085.

Links

Table of n, a(n) for n=1..68.

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, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395

Sequence in context: A011074 A020816 A174860 * A099097 A152150 A136239

Adjacent sequences: A157388 A157389 A157390 * A157392 A157393 A157394

Keyword

easy,nonn,tabl

Author

Peter Luschny, Mar 07 2009, Mar 14 2009

Status

approved