cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A064069 Generalized Euler number c(8,n).

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%I A064069 #21 Feb 16 2025 08:32:45
%S A064069 2,96,29184,22634496,32864600064,76717014122496,262665886073094144,
%T A064069 1239981021847665770496,7719096548270543600615424,
%U A064069 61267211781784116552580202496,603881788505747521507846892027904,7236592671961544936200760521440362496,103612803724706836868168667250308188995584
%N A064069 Generalized Euler number c(8,n).
%H A064069 Matthew House, <a href="/A064069/b064069.txt">Table of n, a(n) for n = 0..176</a>
%H A064069 D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1967-0223295-5">Generalized Euler and class numbers</a>. Math. Comp. 21 (1967) 689-694.
%H A064069 D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1968-0227093-9">Corrigenda to: "Generalized Euler and class numbers"</a>, Math. Comp. 22 (1968), 699.
%H A064069 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EulerNumber.html">Euler Number</a>.
%F A064069 a(n) = 2^(4n+5) * A000281(n).
%F A064069 a(n) = (2*n)!*[x^(2*n)](sec(8*x)*2*cos(4*x)). - _Peter Luschny_, Nov 21 2021
%p A064069 egf := sec(8*x)*2*cos(4*x): ser := series(egf, x, 24):
%p A064069 seq((2*n)!*coeff(ser, x, 2*n), n = 0..11); # _Peter Luschny_, Nov 21 2021
%t A064069 Range[0, 24, 2]! CoefficientList[Series[2 Sec[8 x] Cos[4 x], {x, 0, 24}], x^2] (* _Matthew House_, Oct 25 2024 *)
%Y A064069 Row 8 of A235605.
%Y A064069 Cf. A000281, A064073, A349267, A349264.
%K A064069 nonn,easy
%O A064069 0,1
%A A064069 _Eric W. Weisstein_, Aug 31 2001