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A002454 Central factorial numbers: 4^n (n!)^2.
(Formerly M3693 N1510)
+0
6
1, 4, 64, 2304, 147456, 14745600, 2123366400, 416179814400, 106542032486400, 34519618525593600, 13807847410237440000, 6682998146554920960000, 3849406932415634472960000, 2602199086312968903720960000 (list; graph; listen)
OFFSET

0,2

COMMENT

Denominators in the series for Bessel's J0(x)= 1 -x^2/4 +x^4/64 -x^6/2304 +-...

REFERENCES

Bronstein-Semendjajew, Taschenbuch der Mathematik, 7th german ed. 1965, ch. 4.4.7

A. Fletcher, J. C. P. Miller, L. Rosenhead, and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 110.

E. L. Ince, Ordinary Differential Equations, Dover, NY, 1956; see p. 173.

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

T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. 2, Engelmann, Leipzig, 1880, p. 7.

LINKS

T. D. Noe, Table of n, a(n) for n=0..50

Index entries for sequences related to factorial numbers

FORMULA

(-1)^n*a(n) is the coefficient of x^1 in prod(k=0, 2*n, x+2*k-2*n). - Benoit Cloitre and Michael Somos, Nov 22, 2002.

CROSSREFS

Cf. A000165, A001818.

J1: A002474, J2: A002506, J3: A014401.

Sequence in context: A050636 A098698 A081559 this_sequence A013043 A088065 A053718

Adjacent sequences: A002451 A002452 A002453 this_sequence A002455 A002456 A002457

KEYWORD

nonn,easy

AUTHOR

njas

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.


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