A174491 Denominator in the coefficient of x^n in exp( Sum_{m>=1} x^m/(m*2^(m^2)) ).

1, 2, 32, 512, 262144, 33554432, 137438953472, 562949953421312, 147573952589676412928, 2417851639229258349412352, 2535301200456458802993406410752, 2658455991569831745807614120560689152

Offset

0,2

Comments

It is surprising that these terms should consist only of powers of 2.

Links

Table of n, a(n) for n=0..11.

Formula

a(n) = 2^(n^2)*A006519(n) where A006519(n) = highest power of 2 dividing n [conjecture].

Example

G(x) = exp( x/2 + x^2/(2*2^4) + x^3/(3*2^9) + x^4/(4*2^16) +...)
G(x) = 1 + 1/2*x + 5/32*x^2 + 19/512*x^3 + 1921/262144*x^4 +...

Mathematica

Table[Denominator@ SeriesCoefficient[Exp[Sum[x^m/(m*2^(m^2)), {m, 1, n}]], {x, 0, n}], {n, 0, 11}] (* Michael De Vlieger, May 12 2017 *)

Prog

(PARI) {a(n) = denominator(polcoeff(exp(sum(m=1, n+1, x^m/(m*2^(m^2))) + x*O(x^n)), n))}

Crossrefs

Cf. A174490 (numerators).

Sequence in context: A246213 A022028 A013776 * A022019 A010045 A052151

Adjacent sequences: A174488 A174489 A174490 * A174492 A174493 A174494

Keyword

frac,nonn

Author

Paul D. Hanna, Mar 25 2010

Extensions

Edited by Paul D. Hanna, Mar 29 2010

Status

approved