[seqfan] Sequence to A141530

[vincenzo.librandi at tin.it]

I think that 
a(n)=4*n^3+6*n^2-1
is equal to A141530

           
0          -1
           1           9
           2          55
           3         161
           4         351
           5         
649
           6        1079
           7        1665
           
8        2431
           9        3401
          10        4599
          11        6049
          12        7775
          13        
9801
          14       12151
          15       14849
          
16       17919
          17       21385
          18       25271
          19       29601
          20       34399
          21       
39689
          22       45495
          23       51841
          
24       58751
          25       66249
          26       74359
          27       83105
          28       92511
          29      
102601
          30      113399

Regards,
Vincenzo Librandi

%I A141530
%S A141530 1,1,9,55,161,351,649,1079,1665
%V A141530 1,
-1,9,55,161,351,649,1079,1665
%N A141530 Third from a recurrences 
family concerning numerators of a(i,j) square 
               defined 
by j!*a(i,j)=Integral (from i to i+1) u*(u-1)*(-2)* .. *(u-j+1) 
               du. For recurrences,family begins at j=1 (not 0,hence 
third of the 
               family instead of fourth). j=1: a(n)=a(n-1)
+2, A005408; j=2: a(n)=2a(n-1)-a(n-2)+12, 
               A140811; j=3: 
a(n)=3a(n-1)-3a(n-2)+a(n-3)+24, this sequence; j=4: 
               4a
(n-1)-6a(n-2)+4a(n-3)-a(n-4)+720; j=5: 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)
+a(n-5)+1440; 
               then Pascal A007318 without first 1's, 
signed, followed with A0911317(j). 
               A091137(j) is ALSO a
(i,j) denominators, not A002790 as written in 
               A140825 
modified Aug 6.
%C A141530 Initial terms of every sequence are given by 
triangle online: 1; -1, 
               5; 1, -1, 9;
%Y A141530 Cf. 
A141047, A141417.
%Y A141530 Sequence in context: A058852 A145875 
A068970 this_sequence A016269 A005770 
               A030053
%Y 
A141530 Adjacent sequences: A141527 A141528 A141529 this_sequence 
A141531 A141532 
               A141533
%K A141530 sign,uned
%O A141530 
0,3
%A A141530 Paul Curtz (bpcrtz(AT)free.fr), Aug 12 2008