A064070 Generalized Euler number c(9,n).

2, 126, 49410, 48649086, 89434106370, 264235243691646, 1145011717430672130, 6841110155700330881406, 53899295662946509072626690, 541439307193573593050370186366, 6754273504043546592593642328610050, 102439130403410639137159601119206854526

Offset: 0

Author

Eric W. Weisstein, Aug 31 2001

Keywords

• nonn
• easy

Links

• Matthew House, Table of n, a(n) for n = 0..174
• D. Shanks, Generalized Euler and class numbers. Math. Comp. 21 (1967) 689-694.
• D. Shanks, Corrigenda to: "Generalized Euler and class numbers", Math. Comp. 22 (1968), 699.
• Eric Weisstein's World of Mathematics, Euler Number.

Crossrefs

Row 9 of A235605.

Cf. A064074, A349268, A349264.

Programs

Maple

egf := sec(9*x)*2*cos(3*x)^2: ser := series(egf, x, 24):
seq((2*n)!*coeff(ser, x, 2*n), n = 0..10); # Peter Luschny, Nov 21 2021

Mathematica

Range[0, 22, 2]! CoefficientList[Series[2 Sec[9 x] Cos[3 x]^2, {x, 0, 22}], x^2] (* Matthew House, Oct 27 2024 *)

Formula

a(n) = (2*n)!*[x^(2*n)](sec(9*x)*2*cos(3*x)^2). - Peter Luschny, Nov 21 2021