A159930 Triangle read by rows: a(1,1)=1. a(m,n) = a(m-1,n) + (sum of all terms in row m-1), for n<m. a(m,m) = sum of all terms in row m-1.

1, 2, 1, 5, 4, 3, 17, 16, 15, 12, 77, 76, 75, 72, 60, 437, 436, 435, 432, 420, 360, 2957, 2956, 2955, 2952, 2940, 2880, 2520, 23117, 23116, 23115, 23112, 23100, 23040, 22680, 20160, 204557, 204556, 204555, 204552, 204540, 204480, 204120, 201600

Offset

1,2

Comments

The sum of all terms in row m is (m+1)!/2. So a(m,n) = a(m-1,n) + m!/2, or is m!/2 if n=m.

Sum of m-th row = A001710(m+1). [Klaus Brockhaus, Jun 02 2009]

First column is A014288. - Franklin T. Adams-Watters, Oct 19 2013

Links

Table of n, a(n) for n=1..44.

Example

Triangle starts:
1;
2, 1;
5, 4, 3;
17, 16, 15, 12;
77, 76, 75, 72, 60;

Prog

(Magma) S:=[1]; T:=S; for m in [2..9] do s:=&+T; T:=[ n lt m select T[n]+s else s: n in [1..m] ]; S:=S cat T; end for; S; // Klaus Brockhaus, Jun 02 2009

Crossrefs

Cf. A159927.

Sequence in context: A061579 A094064 A343809 * A058344 A010582 A266628

Adjacent sequences: A159927 A159928 A159929 * A159931 A159932 A159933

Keyword

nonn,tabl

Author

Leroy Quet, Apr 26 2009

Extensions

More terms from Klaus Brockhaus, Jun 02 2009

Status

approved