A158098 Euler transform of triangular powers of 2: [2,2^3,2^6,...,2^(n(n+1)/2),...].

1, 2, 11, 84, 1217, 35630, 2177587, 273084984, 69282922119, 35324981861270, 36099947418619965, 73859427092428467556, 302379428224074427461199, 2476485356209583877951854650, 40569774298249879934939059013965, 1329309152683489963994724570066550944

Offset: 0

Author

Paul D. Hanna, Mar 20 2009

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..81

Crossrefs

Cf. A006125, A158099.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(
      d*2^(d*(d+1)/2), d=numtheory[divisors](j)), j=1..n)/n)
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Jul 28 2017

Mathematica

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];
a /@ Range[0, 20] (* Jean-François Alcover, Nov 20 2020, after Alois P. Heinz *)

PARI

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

Formula

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