login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112707 Triangle built from partial sums of Catalan numbers multiplied by powers of nonpositive numbers. 12

%I

%S 1,1,1,1,0,1,1,2,-1,1,1,-3,7,-2,1,1,11,-33,16,-3,1,1,-31,191,-119,29,

%T -4,1,1,101,-1153,1015,-291,46,-5,1,1,-328,7295,-9191,3293,-579,67,-6,

%U 1,1,1102,-47617,87037,-39715,8171,-1013,92,-7,1,1,-3760,318463,-851186,500957,-123079,17131,-1623,121

%N Triangle built from partial sums of Catalan numbers multiplied by powers of nonpositive numbers.

%C The column sequences (without leading zeros) begin with A000012 (powers of 1), A032357(n)*(-1)^n, A064306(n)*(-1)^n, A112710, A112711, A113264-A113269, for m=0.. 10.

%H W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A112707.text">First 10 rows.</a>

%F a(n, m)=sum(C(k)*(-m)^k, k=0..n-m), with C(k):=A000108(k) (Catalan) if n>m>0; a(n, n)=1, a(n, 0)=1, n>=0; a(n, m)=0 if n<m.

%F G.f. for column m>=0 (without leading zeros): c(-m*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.

%Y Row sums give A112708. Unsigned row sums give A112709.

%Y Cf. A112705 (similar triangle with powers of positive numbers).

%K sign,easy,tabl

%O 0,8

%A _Wolfdieter Lang_, Oct 31 2005

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 25 20:23 EST 2014. Contains 250009 sequences.