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A157398
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A partition product of Stirling_2 type [parameter k = -4] with biggest-part statistic (triangle read by rows).
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10
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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FORMULA
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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).
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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