|
|
A008958
|
|
Triangle of central factorial numbers 4^k T(2n+1, 2n+1-2k).
|
|
10
|
|
|
1, 1, 1, 1, 10, 1, 1, 35, 91, 1, 1, 84, 966, 820, 1, 1, 165, 5082, 24970, 7381, 1, 1, 286, 18447, 273988, 631631, 66430, 1, 1, 455, 53053, 1768195, 14057043, 15857205, 597871, 1, 1, 680, 129948, 8187608, 157280838, 704652312, 397027996, 5380840, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
REFERENCES
|
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
|
|
LINKS
|
Robert James Purser, Mobius Net Cubed-Sphere Gnomonic Grids, U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service, National Centers for Environmental Protection, 2018.
|
|
FORMULA
|
G.f. of i-th right-hand column is x/Product_{j=1..i+1} (1 - (2j-1)^2*x).
|
|
EXAMPLE
|
Triangle begins:
1;
1, 1;
1, 10, 1;
1, 35, 91, 1;
1, 84, 966, 820, 1;
1, 165, 5082, 24970, 7381, 1;
1, 286, 18447, 273988, 631631, 66430, 1;
1, 455, 53053, 1768195, 14057043, 15857205, 597871, 1;
1, 680, 129948, 8187608, 157280838, 704652312, 397027996, 5380840, 1;
(End)
|
|
MATHEMATICA
|
Flatten[Table[Sum[(-1)^(q+1) 4^(p-n) (2p+2q-2n-1)^(2n+1)/((2n+1-2p-q)! q!), {q, 0, n-p}], {n, 0, 8}, {p, 0, n}]] (* Wesley Transue, Jan 21 2012 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|