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A158098 Euler transform of triangular powers of 2: [2,2^3,2^6,...,2^(n(n+1)/2),...]. 1
1, 2, 11, 84, 1217, 35630, 2177587, 273084984, 69282922119, 35324981861270, 36099947418619965, 73859427092428467556, 302379428224074427461199, 2476485356209583877951854650, 40569774298249879934939059013965 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..14.

FORMULA

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

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-Fran├žois Alcover, Nov 20 2020, after Alois P. Heinz *)

PROG

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

CROSSREFS

Cf. A006125, A158099.

Sequence in context: A191805 A279202 A086406 * A104185 A074604 A135404

Adjacent sequences:  A158095 A158096 A158097 * A158099 A158100 A158101

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 20 2009

STATUS

approved

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Last modified October 17 16:06 EDT 2021. Contains 348065 sequences. (Running on oeis4.)