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Search: id:A157403
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| A157403 |
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A partition product of Stirling_2 type [parameter k = 3] with biggest-part statistic (triangle read by rows). |
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11
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| 1, 1, 3, 1, 9, 21, 1, 45, 84, 231, 1, 165, 840, 1155, 3465, 1, 855, 8610, 13860, 20790, 65835, 1, 3843, 64680, 250635, 291060, 460845, 1514205, 1, 21819, 689136, 3969735, 6015240, 7373520, 12113640, 40883535, 1, 114075
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Partition product of prod_{j=0..n-1}((k + 1)*j - 1) and n! at k = 3,
summed over parts with equal biggest part (see the Luschny link).
Underlying partition triangle is A143173.
Same partition product with length statistic is A000369.
Diagonal a(A000217) = A008545
Row sum is A016036.
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LINKS
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Peter Luschny, Counting with Partitions.
Peter Luschny, Generalized Stirling_2 Triangles.
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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}(4*j - 1).
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CROSSREFS
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Cf. A157396, A157397, A157398, A157399, A157400, A080510, A157401, A157402, A157404, A157405
Sequence in context: A121489 A118793 A160568 this_sequence A105951 A038202 A128415
Adjacent sequences: A157400 A157401 A157402 this_sequence A157404 A157405 A157406
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Peter Luschny (peter(AT)luschny.de), Mar 09 2009
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