A156138 Q_{2n+1}(sqrt(2))/sqrt(2) (see A104035).

1, 17, 901, 99917, 18991081, 5514615017, 2270974911661, 1258937450889317, 903952433274722641, 816101554527859690817, 904827968753139590344021, 1208617989532834039606507517, 1914312457105234828011498655801, 3547500444096776665586928259547417, 7604155838367549221056955383942297981

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..207

Formula

E.g.f.: sin(x)/(1 - 3*sin(x)^2) = x + 17*x^3/3! + 901*x^5/5! + 99917*x^7/7! + ... - Peter Bala, Feb 06 2017

Example

G.f. = 1 + 17*x + 901*x^2 + 99917*x^3 + 18991081*x^4 + 5514615017*x^5 + ... - Michael Somos, Aug 19 2018

Maple

with(gfun):
series(sin(x)/(1-3*sin(x)^2), x, 30):
L := seriestolist(%):
seq(op(2*i, L)*(2*i-1)!, i = 1..floor((1/2)*nops(L)));
# Peter Bala, Feb 06 2017

Mathematica

With[{nmax = 50}, CoefficientList[Series[Sin[x]/(1 - 3*Sin[x]^2), {x, 0, nmax}], x]*Range[0, nmax]!][[2 ;; ;; 2]] (* G. C. Greubel, Aug 17 2018 *)

Prog

(PARI) x='x+O('x^50); v=Vec(serlaplace(sin(x)/(1 - 3*sin(x)^2))); vector((#v-1)\2 , n, v[2*n-1]) \\ G. C. Greubel, Aug 17 2018

Crossrefs

Cf. A101923, A000364, A000464, A002439.

Cf. other sequences with a g.f. of the form sin(x)/(1 - k*sin^2(x)): A101923 (k=1/2), A000364 (k=1), A000464 (k=2), A002439 (k=4).

Sequence in context: A124235 A218660 A086265 * A229261 A196873 A262386

Adjacent sequences: A156135 A156136 A156137 * A156139 A156140 A156141

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 06 2009

Status

approved