# [seqfan] Sequence to A141530

vincenzo.librandi at tin.it vincenzo.librandi at tin.it
Thu Feb 12 12:14:04 CET 2009

```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

```