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

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;
  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