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A059369 Triangle of numbers T(n,k) = T(n-1,k-1) + ((n+k-1)/k)*T(n-1,k), n >= 1, 1<=k<=n, with T(n,1) = n!, T(n,n) = 1; read from right to left. 3
1, 1, 2, 1, 4, 6, 1, 6, 16, 24, 1, 8, 30, 72, 120, 1, 10, 48, 152, 372, 720, 1, 12, 70, 272, 828, 2208, 5040, 1, 14, 96, 440, 1576, 4968, 14976, 40320, 1, 16, 126, 664, 2720, 9696, 33192, 115200, 362880, 1, 18, 160, 952, 4380, 17312, 64704, 247968, 996480 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Another version of triangle in A090238 . - Philippe Deléham, Jun 14 2007

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 171, #34.

LINKS

Table of n, a(n) for n=1..54.

FORMULA

G.f. for k-th diagonal: (Sum_{i >= 1} i!*t^i )^k = Sum_{n >= k} T(n, k)*t^n.

T(n,k)=if k=1 then n! else if k=n then 1 else sum(m=0...n-k, (m+1)!T(n-m-1,k-1)); [From Vladimir Kruchinin, Aug 18 2010]

EXAMPLE

When read from left to right the rows {T(n,k), 1<=k<=n} for n=1,2,3,... are 1; 2,1; 6,4,1; 24,16,6,1; ...

MATHEMATICA

nmax = 10; t[n_, k_] := Sum[(m+1)!*t[n-m-1, k-1], {m, 0, n-k}]; t[n_, 1] = n!; t[n_, n_] = 1; Flatten[ Table[ t[n, k], {n, 1, nmax}, {k, n, 1, -1}]] (* Jean-François Alcover, Nov 14 2011 *)

CROSSREFS

Cf. A059370, A059371.

Sequence in context: A062344 A208759 A033877 * A199530 A208765 A232335

Adjacent sequences:  A059366 A059367 A059368 * A059370 A059371 A059372

KEYWORD

nonn,tabl,easy,nice

AUTHOR

N. J. A. Sloane, Jan 28 2001

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Jan 31 2001

STATUS

approved

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)