OFFSET
0,4
COMMENTS
The e.g.f., F(x) = exp(-x)*sum_{n>=0} x^(n*(n+1)/2)/(n*(n+1)/2)!, is approximated by 1/sqrt(2x) for x>1; example: F(1)=0.79758, F(2)=0.59852, F(10)=0.23183, F(50)=0.10063.
FORMULA
E.g.f.: exp(-x)*sum_{n>=0} x^(n*(n+1)/2)/(n*(n+1)/2)!
MATHEMATICA
Table[Sum[(-1)^(n-k) * Binomial[n, k] * SquaresR[1, 8*k+1]/2, {k, 0, n}], {n, 0, 40}] (* Vaclav Kotesovec, Oct 31 2017 *)
PROG
(PARI) {a(n)=n!*polcoeff((sum(k=0, sqrtint(2*n+1), x^(k*(k+1)/2)/(k*(k+1)/2)!)*sum(j=0, n, (-x)^j/j!)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Mar 30 2004
STATUS
approved