The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A002112

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A002112

Glaisher's H numbers.
(history; published version)

#53 by Joerg Arndt at Fri Dec 24 02:31:10 EST 2021

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reviewed

approved

#52 by Michel Marcus at Fri Dec 24 00:28:41 EST 2021

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proposed

reviewed

#51 by Jon E. Schoenfield at Thu Dec 23 22:38:01 EST 2021

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editing

proposed

#50 by Jon E. Schoenfield at Thu Dec 23 22:37:59 EST 2021

FORMULA

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

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#49 by Andrew Howroyd at Thu May 07 11:11:35 EDT 2020

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reviewed

approved

#48 by Joerg Arndt at Thu May 07 06:17:25 EDT 2020

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proposed

reviewed

#47 by Michel Marcus at Thu May 07 05:29:37 EDT 2020

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editing

proposed

#46 by Michel Marcus at Thu May 07 05:29:33 EDT 2020

REFERENCES

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

#45 by Michel Marcus at Thu May 07 05:29:07 EDT 2020

LINKS

J. W. L. Glaisher, <a href="httphttps://doi.org/10.1112/plms.oxfordjournals.org/content/s1-31/.1/.216.extract">On a set of coefficients analogous to the Eulerian numbers</a>, Proc. London Math. Soc., 31 (1899), 216-235.

Michael E. Hoffman, <a href="https://doi.org/10.37236/1453">Derivative polynomials, Euler polynomials, and associated integer sequences</a>, The Electronic Journal of Combinatorics [electronic only] 6.1 (1999).

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).

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proposed

editing

#44 by Vaclav Kotesovec at Thu May 07 04:54:50 EDT 2020

STATUS

editing

proposed