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 A157398 A partition product of Stirling_2 type [parameter k = -4] with biggest-part statistic (triangle read by rows). 10
 1, 1, 4, 1, 12, 28, 1, 72, 112, 280, 1, 280, 1400, 1400, 3640, 1, 1740, 15120, 21000, 21840, 58240, 1, 8484, 126420, 401800, 382200, 407680, 1106560, 1, 57232, 1538208, 6370000, 8357440, 8153600, 8852480, 24344320, 1 (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 A134149. Same partition product with length statistic is A035469. Diagonal a(A000217) = A007559. Row sum is A049119. 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}(-3*j - 1). CROSSREFS Cf. A157396, A157397, A157399, A157400, A080510, A157401, A157402, A157403, A157404, A157405 Sequence in context: A173621 A274087 A105197 * A306299 A089503 A019236 Adjacent sequences:  A157395 A157396 A157397 * A157399 A157400 A157401 KEYWORD easy,nonn,tabl AUTHOR Peter Luschny, Mar 09 2009, Mar 14 2009 STATUS approved

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Last modified August 12 13:34 EDT 2022. Contains 356077 sequences. (Running on oeis4.)