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A172109 T_2(n) gives the number of ordered partitions of {1,1,2,3,...,n-1}. 1
0, 2, 8, 44, 308, 2612, 25988, 296564, 3816548, 54667412, 862440068, 14857100084, 277474957988, 5584100659412, 120462266974148, 2772968936479604, 67843210855558628, 1757952715142990612, 48093560991292628228 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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>=2, T_2(n) = Sum_{m=1..n} Sum_{l=0..m} C(m,l)*C(l+1,2)*(-1)^(m-l)*l^(n-2).

G.f.: 1/G(0) -1  where G(k) = 1 - x*(k+2)/( 1 - 2*x*(k+1)/G(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 23 2013

G.f.: 1/Q(0) -1, where Q(k) = 1 - x*(3*k+2) - 2*x^2*(k+1)*(k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 03 2013

a(n) = Sum_{k=1..n-1} stirling2(n-1,k)*(k+1)!. - Karol A. Penson, Sep 04 2015

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[2, n], {n, 2, 21}]

CROSSREFS

This gives the row sums of A172106.

Cf. A005649. - R. J. Mathar, Jan 28 2010

Sequence in context: A052897 A137984 A191810 * A005649 A253950 A212913

Adjacent sequences:  A172106 A172107 A172108 * A172110 A172111 A172112

KEYWORD

nonn

AUTHOR

Martin Griffiths, Jan 25 2010

STATUS

approved

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Last modified July 17 18:47 EDT 2019. Contains 325109 sequences. (Running on oeis4.)