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A002453 Central factorial numbers.
(Formerly M5249 N2283)
4
1, 35, 966, 24970, 631631, 15857205, 397027996, 9931080740, 248325446061, 6208571999575, 155218222621826, 3880490869237710, 97012589464171291, 2425317596203339145, 60632965641474990456, 1515824372664398367880 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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. 112.

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. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 36.

LINKS

Table of n, a(n) for n=0..15.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for sequences related to factorial numbers

FORMULA

G.f.: 1/((1-x)*(1-9*x)*(1-25*x).

a(n) = 1/384 * (625*25^n - 243*9^n + 2).

E.g.f.: 1/120*sinh(x)^5 = sum{n>=0, a(n)*x^(2*n+5)/(2*n+5)!} [Vladimir Kruchinin, Sep 30 2012]

a(n) = det(|v(i+3,j+2)|, 1 <= i,j <= n), where v(n,k) are central factorial numbers of the first kind with odd indices (A008956). [Mircea Merca, Apr 06 2013]

MAPLE

A002453:=-1/(z-1)/(25*z-1)/(9*z-1); [By Simon Plouffe in his 1992 dissertation.]

CROSSREFS

Right-hand column 2 in triangle A008958.

Sequence in context: A080250 A014934 A115473 * A210313 A049395 A215296

Adjacent sequences:  A002450 A002451 A002452 * A002454 A002455 A002456

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified April 17 07:00 EDT 2014. Contains 240634 sequences.