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A002454 Central factorial numbers: 4^n (n!)^2.
(Formerly M3693 N1510)
8
1, 4, 64, 2304, 147456, 14745600, 2123366400, 416179814400, 106542032486400, 34519618525593600, 13807847410237440000, 6682998146554920960000, 3849406932415634472960000, 2602199086312968903720960000 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

COMMENTS

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.

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).

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 to divisibility sequences

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.

E.g.f A(x)=arcsin(x)*sec(arcsin(x)). [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 12 2010]

E.g.f.: arcsin(x)*sec(arcsin(x))=arcsin(x)/sqrt(1-x^2)=x/G(0);  G(k)=2k*(x^2+1)+1-x^2*(2k+1)*(2k+2)/G(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Nov 20 2011

CROSSREFS

Cf. A000165, A001818.

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

Sequence in context: A098698 A181398 A081559 * A013043 A167406 A156631

Adjacent sequences:  A002451 A002452 A002453 * A002455 A002456 A002457

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified February 17 21:13 EST 2012. Contains 206085 sequences.