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 A157401 A partition product of Stirling_2 type [parameter k = 1] with biggest-part statistic (triangle read by rows). 10
 1, 1, 1, 1, 1, 3, 3, 1, 9, 12, 15, 1, 25, 60, 75, 105, 1, 75, 330, 450, 630, 945, 1, 231, 1680, 3675, 4410, 6615, 10395, 1, 763, 9408, 30975, 41160, 52920, 83160, 135135, 1, 2619, 56952, 233415, 489510, 555660, 748440, 1216215 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 1, summed over parts with equal biggest part (see the Luschny link). Underlying partition triangle is A143171. Same partition product with length statistic is A001497. Diagonal a(A000217) = A001147. Row sum is A001515. 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}(2*j - 1). CROSSREFS Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157402, A157403, A157404, A157405 Sequence in context: A188513 A260301 A216916 * A143911 A185422 A131889 Adjacent sequences:  A157398 A157399 A157400 * A157402 A157403 A157404 KEYWORD easy,nonn,tabl AUTHOR Peter Luschny, Mar 09 2009, Mar 14 2009 STATUS approved

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