A383928 Expansion of g.f. cosh(9*arctanh(4*sqrt(x))).

1, 648, 76896, 4601088, 194102784, 6662320128, 199818854400, 5451206492160, 138644854013952, 3341194489757696, 77151510667984896, 1720777996555517952, 37293854107184922624, 788969931176505507840, 16350749459194860011520, 332885987884833366343680, 6673058165121160335851520

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = 4^n*(105 + 400*n + 3392*n^2 + 512*n^3 + 4096*n^4)*(2*n)!/(105*(n!)^2).

O.g.f.: (1 + 576*x + 32256*x^2 + 344064*x^3 + 589824*x^4)/(-16*x + 1)^(9/2).

E.g.f.: 134217728*((x^4 + 41/128*x^3 + 425/16384*x^2 + 525/1048576*x + 105/134217728)*BesselI(0, 8*x) + x*BesselI(1, 8*x)*(x^3 + 33/128*x^2 + 193/16384*x + 25/1048576))*exp(8*x)/105.

Maple

seq(coeff(series((589824*x^4 + 344064*x^3 + 32256*x^2 + 576*x + 1)/(-16*x + 1)^(9/2), x, 17), x, k), k=0..16);

Crossrefs

Cf. A285043, A285044, A285045, A285046.

Sequence in context: A185270 A250343 A035755 * A107551 A202056 A229155

Adjacent sequences: A383925 A383926 A383927 * A383929 A383930 A383931

Keyword

nonn,easy

Author

Karol A. Penson, May 15 2025

Status

approved