A335749 a(n) = n!*[x^n] exp(2*x)*(y*sinh(x*y) + cosh(x*y)) and y = sqrt(6).

1, 8, 34, 152, 676, 3008, 13384, 59552, 264976, 1179008, 5245984, 23341952, 103859776, 462123008, 2056211584, 9149092352, 40708792576, 181133355008, 805951005184, 3586070730752, 15956184933376, 70996881195008, 315899894646784, 1405593340977152, 6254173153202176

Offset: 0

Author

Peter Luschny, Jun 24 2020

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,2).

Crossrefs

Cf. A335312.

Programs

Maple

aList := proc(len) local H; H := (x, y) -> exp(2*x)*(y*sinh(x*y) + cosh(x*y)):
series(H(x, sqrt(6)), x, len + 1): seq(k!*coeff(%, x, k), k=0..len-1) end:
aList(25);

Mathematica

LinearRecurrence[{4, 2}, {1, 8}, 30] (* Paolo Xausa, Feb 01 2024 *)

PARI

Vec((1 + 4*x) / (1 - 4*x - 2*x^2) + O(x^25)) \\ Colin Barker, Jun 25 2020

Formula

a(n) = A335312(n, 6).

From Colin Barker, Jun 24 2020: (Start)

G.f.: (1 + 4*x) / (1 - 4*x - 2*x^2) for n>1.

a(n) = 4*a(n-1) + 2*a(n-2). (End)

a(n) = 4*A090017(n)+A090017(n+1). - R. J. Mathar, Mar 10 2022