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A125178 Triangle read by rows: T(n,0)=B(n) (the Bell numbers, A000110(n)), T(n,k)=0 for k<0 or k>n, T(n,k)=T(n-1,k)+T(n-1,k-1) for n>=1, 0<=k<=n. 1
1, 1, 1, 2, 2, 1, 5, 4, 3, 1, 15, 9, 7, 4, 1, 52, 24, 16, 11, 5, 1, 203, 76, 40, 27, 16, 6, 1, 877, 279, 116, 67, 43, 22, 7, 1, 4140, 1156, 395, 183, 110, 65, 29, 8, 1, 21147, 5296, 1551, 578, 293, 175, 94, 37, 9, 1, 115975, 26443, 6847, 2129, 871, 468, 269, 131, 46, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums = 1, 2, 5, 13, 36, 109, 369,...

Columns 0,1 and 2 yield A000110,A005001 and A029761, respectively.

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

First few rows of the triangle are:

1;

1, 1;

2, 2, 1;

5, 4, 3, 1;

15, 9, 7, 4, 1;

52, 24, 16, 11, 5, 1;

203, 76, 40, 27, 16, 6, 1;

...

(4,3) = 16 = 7 + 9 = (3,3) + (3,2).

MAPLE

with(combinat): T:=proc(n, k) if k=0 then bell(n) elif k<0 or k>n then 0 else T(n-1, k)+T(n-1, k-1) fi end: for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form

CROSSREFS

Cf. A000110, A005001, A029761.

Sequence in context: A273342 A276067 A125177 * A101975 A136388 A099605

Adjacent sequences:  A125175 A125176 A125177 * A125179 A125180 A125181

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 22 2006

EXTENSIONS

Edited by N. J. A. Sloane, Nov 29 2006

STATUS

approved

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Last modified October 20 05:31 EDT 2018. Contains 316378 sequences. (Running on oeis4.)