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
Programs
-
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);
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.