A157384 A partition product of Stirling_1 type [parameter k = -4] with biggest-part statistic (triangle read by rows).

1, 1, 4, 1, 12, 20, 1, 72, 80, 120, 1, 280, 1000, 600, 840, 1, 1740, 9200, 9000, 5040, 6720, 1, 8484, 79100, 138600, 88200, 47040, 60480, 1, 57232, 874720, 1789200, 1552320, 940800, 483840, 604800, 1, 328752, 9532880

Offset

1,3

Comments

Partition product of prod_{j=0..n-2}(k-n+j+2) and n! at k = -4,

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

Underlying partition triangle is A144354.

Same partition product with length statistic is A049352.

Diagonal a(A000217(n)) = rising_factorial(4,n-1), A001715(n+2).

Row sum is A049377.

Links

Table of n, a(n) for n=1..39.

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-2).

Crossrefs

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

Sequence in context: A187541 A117413 A322970 * A173621 A274087 A105197

Adjacent sequences: A157381 A157382 A157383 * A157385 A157386 A157387

Keyword

easy,nonn,tabl

Author

Peter Luschny, Mar 07 2009, Mar 14 2009

Status

approved