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 A157383 A partition product of Stirling_1 type [parameter k = -3] with biggest-part statistic (triangle read by rows). 10
 1, 1, 3, 1, 9, 12, 1, 45, 48, 60, 1, 165, 480, 300, 360, 1, 855, 3840, 3600, 2160, 2520, 1, 3843, 29400, 46200, 30240, 17640, 20160, 1, 21819, 272832, 520800, 443520, 282240, 161280, 181440 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Partition product of 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 A144353. Same partition product with length statistic is A046089. Diagonal a(A000217(n)) = rising_factorial(3,n-1), A001710(n+1). Row sum is A049376. LINKS 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-1). CROSSREFS Cf. A157386, A157385, A157384, A157400, A126074, A157391, A157392, A157393, A157394, A157395 Sequence in context: A260285 A242499 A173020 * A232598 A174510 A141237 Adjacent sequences:  A157380 A157381 A157382 * A157384 A157385 A157386 KEYWORD easy,nonn,tabl AUTHOR Peter Luschny, Mar 07 2009, Mar 14 2009 STATUS approved

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Last modified October 14 07:00 EDT 2019. Contains 327995 sequences. (Running on oeis4.)