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A002112 Glaisher's H numbers.
(Formerly M3135 N1272)
4
3, 33, 903, 46113, 3784503, 455538993, 75603118503, 16546026500673, 4616979073434903, 1599868423237443153, 674014138103352845703, 339274210193051498798433, 201097637653063767131142903, 138634566390566081044811718513 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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. 76.

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

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).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

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

Michael E. Hoffman, Derivative polynomials, Euler polynomials, and associated integer sequences, The Electronic Journal of Combinatorics [electronic only] 6.1 (1999)

Index entries for sequences related to Glaisher's numbers

FORMULA

H(n)=2^(2n+1)*I(n), where e.g.f. for (-1)^n*I(n) is (3/2)/(1+exp(x)+exp(-x)) (see A047788, A047789).

H(n) = 3* A000436(n)/2^(2n+1)= 3*A002114(n). - Philippe Deléham, Jan 17 2004

E.g.f.: E(x)= 3*x^2/(G(0)-x^2) ; G(k)= 2*(2*k+1)*(k+1) - x^2 + 2*x^2*(2*k+1)*(k+1)/G(k+1); (continued fraction Euler's kind, 1-step ).- Sergei N. Gladkovskii, Jan 03 2012

If E(x) = Sum(k=0,1,..., a(k+1)*x^(2k+2 )), then A002112(k) = a(k+1)*(2*k+2)!. - Sergei N. Gladkovskii, Jan 09 2012

MATHEMATICA

e[0] = 1; e[n_] := e[n] = (-1)^n*(1 - Sum[(-1)^i*Binomial[2n, 2i]*3^(2n-2i)*e[i], {i, 0, n-1}]); a[n_] := 3*e[n]/2^(2n+1); Table[a[n], {n, 1, 14}] (* Jean-François Alcover, Jan 31 2012, after Philippe Deléham *)

CROSSREFS

Sequence in context: A124432 A234715 A126466 * A055549 A086894 A255930

Adjacent sequences:  A002109 A002110 A002111 * A002113 A002114 A002115

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 19 13:02 EST 2019. Contains 320310 sequences. (Running on oeis4.)