0,2

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, Messenger of Math., 28 (1898), 36-79, see esp. p. 76.

J. W. L. Glaisher, On the Bernoullian function, Q. J. Pure Appl. Math., 29 (1898), 1-168.

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).

T. D. Noe, Table of n, a(n) for n=0..100

Michael E. Hoffman, DERIVATIVE POLYNOMIALS, EULER POLYNOMIALS, AND ASSOCIATED INTEGER SEQUENCES

Index entries for sequences related to Glaisher's numbers

G. E. Andrews, J. Jimenez-Urroz, K. Ono, q-series identities and values of certain L-functions, Duke Math J., Volume 108, No.3 (2001), 395-419. [From Peter Bala (pbala(AT)talktalk.net), Mar 24 2009]

Q_{2n+1)(sqrt(3))/sqrt(3), where the polynomials Q_n() are defined in A104035. - njas, Nov 06 2009

E.g.f.: sin(2*x)/(2*cos(3*x)) = Sum a(n)*x^(2*n-1)/(2*n-1)!.

With offset 1 instead of 0: a(1)=1, a(n)=(-4)^(n-1) - Sum_{k=1..n} (-9)^k*C(2*n-1, 2*k)*a(n-k).

a(n) = (-1)^(n+1)*(1/12)*E_{2n+1}*6^(2*n+1), where E_m are the Euler numbers. - R. W. Gosper Aug 08, 2001

Contribution from Peter Bala (pbala(AT)talktalk.net), Mar 24 2009: (Start)

Basic hypergeometric generating function: exp(-t)*Sum {n = 0..inf} Product {k = 1..n} (1-exp(-24*k*t)) = 1 + 23*t + 1681*t^2/2! + .... For other sequences with generating functions of a similar type see A000364, A000464, A002105, A079144, A158690.

a(n) = (1/2)*(-1)^(n+1)*L(-2*n-1), where L(s) is a Dirichlet L-function for a Dirichlet character with modulus 12: L(s) = 1 - 1/5^s - 1/7^s + 1/11^s + - - + .... See the Andrew's link. (End)

With offset 1 instead of 0: A002439:=proc(n) option remember; if n=1 then 1 else (-4)^(n-1) - add( (-9)^k*binomial(2*n-1, 2*k)*A002439(n-k), k=1..n); fi; end;

(PARI) a(n)=if(n<2, n>0, (-4)^(n-1)-sum(k=1, n, (-9)^k*C(2*n-1, 2*k)*a(n-k)))

Cf. A000364, A000464, A002105, A079144, A158690. [From Peter Bala (pbala(AT)talktalk.net), Mar 24 2009]

Bisections: A156175, A156176. Twice this sequence gives A000191.

Sequence in context: A049003 A003281 A034243 this_sequence A132395 A064016 A138735

Adjacent sequences: A002436 A002437 A002438 this_sequence A002440 A002441 A002442

nonn,easy,nice,new

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Michael Somos