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A158098 Euler transform of triangular powers of 2: [2,2^3,2^6,...,2^(n(n+1)/2),...]. 2
1, 2, 11, 84, 1217, 35630, 2177587, 273084984, 69282922119, 35324981861270, 36099947418619965, 73859427092428467556, 302379428224074427461199, 2476485356209583877951854650, 40569774298249879934939059013965, 1329309152683489963994724570066550944 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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-François 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
Sequence in context: A363563 A279202 A086406 * A104185 A074604 A135404
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 20 2009
STATUS
approved

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Last modified June 22 02:28 EDT 2024. Contains 373561 sequences. (Running on oeis4.)