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 A157397 A partition product of Stirling_2 type [parameter k = -5] with biggest-part statistic (triangle read by rows). 10
 1, 1, 5, 1, 15, 45, 1, 105, 180, 585, 1, 425, 2700, 2925, 9945, 1, 3075, 34650, 52650, 59670, 208845, 1, 15855, 308700, 1248975, 1253070, 1461915, 5221125, 1, 123515, 4475520, 23689575, 33972120, 35085960, 41769000 (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 = -5, summed over parts with equal biggest part (see the Luschny link). Underlying partition triangle is A134273. Same partition product with length statistic is A049029. Diagonal a(A000217) = A007696. Row sum is A049120. 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}(-4*j - 1). CROSSREFS Cf. A157396, A157398, A157399, A157400, A080510, A157401, A157402, A157403, A157404, A157405 Sequence in context: A264616 A157395 A157385 * A157405 A283434 A019429 Adjacent sequences:  A157394 A157395 A157396 * A157398 A157399 A157400 KEYWORD easy,nonn,tabl AUTHOR Peter Luschny, Mar 09 2009 EXTENSIONS Offset corrected by Peter Luschny, Mar 14 2009 STATUS approved

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Last modified October 22 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)