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A172111 T_4(n) gives the number of ordered partitions of {1,1,1,1,2,3,...,n-3}. 1
0, 0, 0, 8, 48, 368, 3408, 36848, 454608, 6294128, 96556368, 1624775408, 29744591568, 588384837488, 12503968334928, 284065406275568, 6869235761650128, 176150548586638448, 4774198652678411088 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..19.

M. Griffiths, I. Mezo, A generalization of Stirling Numbers of the Second Kind via a special multiset, JIS 13 (2010) #10.2.5.

FORMULA

For n>=4, T_4(n) = Sum_{m=1..n} Sum_{l=0..m} binomial(m,l)*binomial(l+3,4)*(-1)^(m-l)*l^(n-4).

MATHEMATICA

f[r_, n_] := Sum[Sum[Binomial[m, l] Binomial[l + r - 1, r] (-1)^(m - l) l^(n - r), {l, 1, m}], {m, 1, n}]; Table[f[4, n], {n, 4, 21}]

CROSSREFS

This gives the row sums of A172108.

Sequence in context: A025013 A215706 A200161 * A144014 A131681 A077708

Adjacent sequences:  A172108 A172109 A172110 * A172112 A172113 A172114

KEYWORD

nonn

AUTHOR

Martin Griffiths, Jan 25 2010

STATUS

approved

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Last modified September 20 01:15 EDT 2020. Contains 337233 sequences. (Running on oeis4.)