A001587 Generalized Euler numbers. (Formerly M1715 N0679)

2, 6, 46, 522, 7970, 152166, 3487246, 93241002, 2849229890, 97949265606, 3741386059246, 157201459863882, 7205584123783010, 357802951084619046, 19133892392367261646, 1096291279711115037162, 67000387673723462963330, 4350684698032741048452486, 299131045427247559446422446

Offset

0,1

Comments

These numbers are related to the values at negative integers of the L-functions for two primitive Dirichlet characters of conductor 24. - F. Chapoton, Oct 05 2020

References

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

Lars Blomberg, Table of n, a(n) for n = 0..199

LMFDB, character 24.5

LMFDB, character 24.11

D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967) 689-694.

D. Shanks, Corrigendum: Generalized Euler and class numbers, Math. Comp. 22, (1968) 699.

D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 689-694; 22 (1968), 699. [Annotated scanned copy]

Formula

E.g.f.: 2 (sin(3 x) + cos(3 x)) / (2 cos(4 x) - 1). - F. Chapoton, Oct 06 2020

a(n) ~ 2^(2*n + 2) * 3^(n + 1/2) * n^(n + 1/2) / (exp(n) * Pi^(n + 1/2)). - Vaclav Kotesovec, Nov 05 2021

a(n) = n!*[x^n](sec(6*x)*(sin(x) + sin(5*x) + cos(x) + cos(5*x))). - Peter Luschny, Nov 21 2021

Maple

egf := sec(6*x)*(sin(x) + sin(5*x) + cos(x) + cos(5*x)): ser := series(egf, x, 20): seq(n!*coeff(ser, x, n), n = 0..17); # Peter Luschny, Nov 21 2021

Prog

(Sage)
t = PowerSeriesRing(QQ, 't').gen()
f = 2 * (sin(3 * t) + cos(3 * t)) / (2 * cos(4 * t) - 1)
f.egf_to_ogf().list() # F. Chapoton, Oct 06 2020

Crossrefs

Bisections are A000192 and A000411. Overview in A349264.

Similar sequences: A000111, A225147.

Sequence in context: A052811 A078603 A316073 * A306784 A078537 A145502

Adjacent sequences: A001584 A001585 A001586 * A001588 A001589 A001590

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(11)-a(14) from Lars Blomberg, Sep 10 2015

Status

approved