The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A293202 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} Sum_{j=0..k} j!*x^(j*i). 7
1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 3, 2, 0, 1, 1, 3, 2, 2, 0, 1, 1, 3, 8, 6, 3, 0, 1, 1, 3, 8, 6, 7, 4, 0, 1, 1, 3, 8, 30, 13, 12, 5, 0, 1, 1, 3, 8, 30, 13, 24, 13, 6, 0, 1, 1, 3, 8, 30, 133, 48, 37, 22, 8, 0, 1, 1, 3, 8, 30, 133, 48, 61, 46, 26, 10, 0, 1, 1, 3, 8, 30, 133, 768, 181, 142, 98, 42, 12, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,13
LINKS
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, ...
0, 1, 3, 3, 3, ...
0, 2, 2, 8, 8, ...
0, 2, 6, 6, 30, ...
0, 3, 7, 13, 13, ...
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1, k)*j!, j=0..min(k, n/i))))
end:
A:= (n, k)-> b(n$2, k):
seq(seq(A(n, d-n), n=0..d), d=0..12); # Alois P. Heinz, Oct 02 2017
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i j, i - 1, k] j!, {j, 0, Min[k, n/i]}]]];
A [n_, k_] := b[n, n, k];
Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Dec 06 2019, after Alois P. Heinz *)
CROSSREFS
Columns k=0..5 give A000007, A000009, A293204, A289485, A289486, A293250.
Rows n=0..1 give A000012, A057427.
Main diagonal gives A161779.
Sequence in context: A303913 A117406 A290216 * A280265 A292795 A295028
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Oct 02 2017
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 12 23:46 EDT 2024. Contains 373362 sequences. (Running on oeis4.)