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A047788 Numerators of Glaisher's I-numbers. 5
1, 1, 1, 7, 809, 1847, 55601, 6921461, 126235201, 8806171927, 2288629046003, 80348736972167, 10111159088668001, 40453941942593304589, 258227002122139705201, 51215766794507248883047, 34747165199239302488636803, 2962605017328303351107945687 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Robert Israel, Table of n, a(n) for n = 0..255

J. W. L. Glaisher, On a set of coefficients analogous to the Eulerian numbers, Proc. London Math. Soc., 31 (1899), 216-235.

Index entries for sequences related to Glaisher's numbers

FORMULA

E.g.f. for (-1)^n*I(n) is (3/2)/(1 + 2*cosh(x)).

EXAMPLE

1/2, 1/3, 1, 7, 809/9, 1847, 55601, 6921461/3, ...

MAPLE

S:= series(3/(2+4*cos(x)), x, 101):

seq(numer(coeff(S, x, 2*j)*(2*j)!), j=0..50); # Robert Israel, Aug 14 2018

MATHEMATICA

terms = 20; CoefficientList[(3/2)/(1+Exp[x]+Exp[-x]) + O[x]^(2terms), x]* Range[0, 2terms-2]! // Abs // Numerator // DeleteCases[#, 0]& (* Jean-Fran├žois Alcover, Feb 28 2019 *)

PROG

(PARI) a(n)=if(n<1, (n==0), n*=2; numerator(n!* polcoeff(3/(2+4*cos(x+O(x^n) )), n))) /* Michael Somos, Feb 26 2004 */

(MAGMA) m:=60; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 3/(2*(1+2*Cosh(x))) )); [Numerator((-1)^(n+1)*Factorial(2*n-2)* b[2*n-1]): n in [1..Floor((m-2)/2)]]; // G. C. Greubel, May 17 2019

(Sage) m = 30; T = taylor(3/(2*(1+2*cosh(x))), x, 0, 2*m+2); [numerator((-1)^n*factorial(2*n)*T.coefficient(x, 2*n)) for n in (0..m)] # G. C. Greubel, May 17 2019

CROSSREFS

Cf. A047789, A002111.

Sequence in context: A001467 A278438 A279120 * A251698 A203694 A269896

Adjacent sequences:  A047785 A047786 A047787 * A047789 A047790 A047791

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 14 16:48 EDT 2019. Contains 328022 sequences. (Running on oeis4.)