A174490 Numerator in the coefficient of x^n in exp( Sum_{m>=1} x^m/(m*2^(m^2)) ).

1, 1, 5, 19, 1921, 42253, 26628779, 15317124535, 521786071318529, 1038675077390118457, 124715000994291451743437, 14203783261714481442742242211, 49356730516809227634074385356860075

Offset

0,3

Links

Table of n, a(n) for n=0..12.

Formula

Denominators are A174491(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[Numerator@ SeriesCoefficient[Exp[Sum[x^m/(m*2^(m^2)), {m, 1, n}]], {x, 0, n}], {n, 0, 12}] (* Michael De Vlieger, May 12 2017 *)

Prog

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

Crossrefs

Cf. A174491.

Sequence in context: A119964 A270477 A279256 * A280034 A270486 A278562

Adjacent sequences: A174487 A174488 A174489 * A174491 A174492 A174493

Keyword

frac,nonn

Author

Paul D. Hanna, Mar 25 2010

Extensions

Edited by Paul D. Hanna, Mar 29 2010

Status

approved