A008958 - OEIS

A008958

Triangle of central factorial numbers 4^k T(2n+1, 2n+1-2k).

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

Table of n, a(n) for n=0..44.

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

From Wesley Transue, Jan 21 2012: (Start)

Triangle begins:

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

Cf. A008955-A008957, A036969.

Columns include A000447. Right-hand columns include A002452, A002453.

Sequence in context: A173047 A173045 A176491 * A168524 A157277 A157629

Adjacent sequences: A008955 A008956 A008957 * A008959 A008960 A008961

KEYWORD

nonn,tabl,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vladeta Jovovic, Apr 16 2000

STATUS

approved