login
Expansion of e.g.f. exp(Sum_{i>=1} Sum_{j=1..i-1} x^(i*j) / (i*j)).
1

%I #4 Oct 06 2019 03:56:17

%S 1,0,1,2,9,44,385,1854,23233,153656,2151441,18787130,338487721,

%T 3165541092,60609811249,835202858294,14913805143105,228441779869424,

%U 5319673396479073,81040768940877426,2153026504862728201,39759334398324543260,988919906784578473761

%N Expansion of e.g.f. exp(Sum_{i>=1} Sum_{j=1..i-1} x^(i*j) / (i*j)).

%F E.g.f.: exp(Sum_{k>=1} floor(A000005(k)/2) * x^k / k).

%F E.g.f.: exp(Sum_{k>=1} A056924(k) * x^k / k).

%F E.g.f.: Product_{k>=1} 1 / (1 - x^A026424(k))^(1/A026424(k)).

%t nmax = 22; CoefficientList[Series[Exp[Sum[Floor[DivisorSigma[0, k]/2] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

%t a[n_] := a[n] = If[n == 0, 1, Sum[Floor[DivisorSigma[0, k]/2] a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 22}]

%Y Cf. A000005, A026424, A028342, A056924, A206303, A327927.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Sep 30 2019