A158098 - OEIS

%I #11 Apr 27 2022 13:21:45

%S 1,2,11,84,1217,35630,2177587,273084984,69282922119,35324981861270,

%T 36099947418619965,73859427092428467556,302379428224074427461199,

%U 2476485356209583877951854650,40569774298249879934939059013965,1329309152683489963994724570066550944

%N Euler transform of triangular powers of 2: [2,2^3,2^6,...,2^(n(n+1)/2),...].

%H Alois P. Heinz, <a href="/A158098/b158098.txt">Table of n, a(n) for n = 0..81</a>

%F G.f.: A(x) = 1/Product_{n>=1} (1 - x^n)^(2^(n(n+1)/2)).

%p a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(

%p       d*2^(d*(d+1)/2), d=numtheory[divisors](j)), j=1..n)/n)

%p     end:

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Jul 28 2017

%t a[n_] := a[n] = If[n==0, 1, Sum[a[n-j] Sum[d 2^(d(d+1)/2), {d, Divisors[j]}], {j, 1, n}]/n];

%t a /@ Range[0, 20] (* _Jean-François Alcover_, Nov 20 2020, after _Alois P. Heinz_ *)

%o (PARI) a(n)=polcoeff(1/prod(k=1,n,(1-x^k+x*O(x^n))^(2^(k*(k+1)/2))),n)

%Y Cf. A006125, A158099.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 20 2009