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A335749 a(n) = n!*[x^n] exp(2*x)*(y*sinh(x*y) + cosh(x*y)) and y = sqrt(6). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,2).

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

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);

PROG

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

CROSSREFS

Cf. A335312.

Sequence in context: A224240 A101644 A126395 * A227330 A252934 A229398

Adjacent sequences:  A335746 A335747 A335748 * A335750 A335751 A335752

KEYWORD

nonn,easy

AUTHOR

Peter Luschny, Jun 24 2020

STATUS

approved

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Last modified August 10 10:09 EDT 2022. Contains 356039 sequences. (Running on oeis4.)