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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

Index to sequences with linear recurrences with constant coefficients, signature (35,-259,225).

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]

a(0)=1, a(1)=35, a(2)=966, a(n)=35*a(n-1)-259*a(n-2)+225*a(n-3). - Harvey P. Dale, Feb 25 2015

MAPLE

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

MATHEMATICA

CoefficientList[Series[1/((1-x)(1-9x)(1-25x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{35, -259, 225}, {1, 35, 966}, 20] (* Harvey P. Dale, Feb 25 2015 *)

CROSSREFS

Right-hand column 2 in triangle A008958.

Sequence in context: A080250 A014934 A115473 * A240826 A210313 A049395

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 26 08:26 EDT 2015. Contains 257081 sequences.