A001823 Central factorial numbers: column 2 in triangle A008956. (Formerly M4671 N1998)

0, 9, 259, 1974, 8778, 28743, 77077, 179452, 375972, 725781, 1312311, 2249170, 3686670, 5818995, 8892009, 13211704, 19153288, 27170913, 37808043, 51708462, 69627922, 92446431, 121181181, 157000116, 201236140, 255401965, 321205599, 400566474, 495632214

Offset

1,2

References

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Formula

a(n) = n*(n-1)*(2*n+1)*(2*n-1)*(2*n-3)*(10*n+7)/90.

If we replace n with n-1/2 in this formula we get 16*A000586(n).

G.f.: z*(9+196*z+350*z**2+84*z**3+z**4)/(1-z)^7.

a(1)=0, a(2)=9, a(3)=259, a(4)=1974, a(5)=8778, a(6)=28743, a(7)=77077, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Harvey P. Dale, Jun 09 2013

Maple

A001823:=-(9+196*z+350*z**2+84*z**3+z**4)/(z-1)**7; # conjectured (correctly) by Simon Plouffe in his 1992 dissertation

Mathematica

Table[1/90*n*(n - 1)*(2*n + 1)*(2*n - 1)*(2*n - 3)*(10*n + 7), {n, 40}] (* Stefan Steinerberger, Apr 15 2006 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 9, 259, 1974, 8778, 28743, 77077}, 30] (* Harvey P. Dale, Jun 09 2013 *)

Crossrefs

A bisection of A181888.

Column 2 in triangle A008956.

Sequence in context: A160073 A157575 A072158 * A229259 A117796 A117051

Adjacent sequences: A001820 A001821 A001822 * A001824 A001825 A001826

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Stefan Steinerberger, Apr 15 2006

Status

approved