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 A157395 A partition product of Stirling_1 type [parameter k = 5] with biggest-part statistic (triangle read by rows). 11
 1, 1, 5, 1, 15, 20, 1, 105, 80, 60, 1, 425, 1200, 300, 120, 1, 3075, 10400, 5400, 720, 120, 1, 15855, 102200, 75600, 15120, 840, 0, 1, 123515, 1149120, 907200, 241920, 20160, 0, 0, 1, 757755, 12783680, 13426560, 3719520, 362880 (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 = 5, summed over parts with equal biggest part (see the Luschny link). Underlying partition triangle is A144879. Same partition product with length statistic is A049411. Diagonal a(A000217(n)) = falling_factorial(5,n-1), row in A008279 Row sum is A049428. 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+7). CROSSREFS Cf. A157386, A157385, A157384, A157383, A157400, A157391, A157392, A157393, A157394, A157395 Sequence in context: A213590 A185263 A264616 * A157385 A157397 A157405 Adjacent sequences:  A157392 A157393 A157394 * A157396 A157397 A157398 KEYWORD easy,nonn,tabl AUTHOR Peter Luschny, Mar 07 2009, Mar 14 2009 STATUS approved

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Last modified October 14 07:11 EDT 2019. Contains 327995 sequences. (Running on oeis4.)