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 A157404 A partition product of Stirling_2 type [parameter k = 4] with biggest-part statistic (triangle read by rows). 10
 1, 1, 4, 1, 12, 36, 1, 72, 144, 504, 1, 280, 1800, 2520, 9576, 1, 1740, 22320, 37800, 57456, 229824, 1, 8484, 182700, 864360, 1005480, 1608768, 6664896, 1, 57232, 2380896, 16546320, 26276544, 32175360, 53319168, 226606464 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 4, summed over parts with equal biggest part (see the Luschny link). Underlying partition triangle is A144267. Same partition product with length statistic is A011801. Diagonal a(A000217) = A008546. Row sum is A028575. LINKS Peter Luschny, Counting with Partitions. Peter Luschny, Generalized Stirling_2 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-1}(5*j - 1). CROSSREFS Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157405 Sequence in context: A019237 A019238 A299523 * A135704 A002564 A287640 Adjacent sequences:  A157401 A157402 A157403 * A157405 A157406 A157407 KEYWORD easy,nonn,tabl AUTHOR Peter Luschny, Mar 09 2009 STATUS approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)