login
Euler transform of 5 4 3 2 1 1 1 1 1 1 1 ...
2

%I #14 May 31 2019 11:28:16

%S 1,5,19,58,157,384,875,1875,3828,7491,14147,25886,46084,80040,135996,

%T 226502,370492,596064,944557,1475983,2276771,3470030,5229835,7800045,

%U 11520003,16858149,24457202,35192852,50251566,71230985,100271453,140224607,194871974

%N Euler transform of 5 4 3 2 1 1 1 1 1 1 1 ...

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F a(n) ~ exp(Pi*sqrt(2*n/3)) * 9*sqrt(3)*n^4 / (4*Pi^10). - _Vaclav Kotesovec_, May 31 2019

%t nmax = 50; CoefficientList[Series[1/((1-x)^4*(1-x^2)^3*(1-x^3)^2*(1-x^4)) * Product[1/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, May 31 2019 *)

%Y Cf. A029859, A029860.

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

%E a(0) = 1 prepended by _Vaclav Kotesovec_, May 31 2019

%E More terms from _Vaclav Kotesovec_, May 31 2019