OFFSET
0,2
COMMENTS
Compare to the e.g.f. of A005651 (sum of multinomial coefficients): Product_{n>=1} 1/(1 - x^n/n!).
FORMULA
a(n) ~ c * n! * n, where c = Product_{k>=2} (1 - 1/k!)^(2^k) = 200.80872040834836274... - Vaclav Kotesovec, Jul 21 2019
EXAMPLE
E.g.f.: A(x) = 1 + 2*x + 10*x^2/2! + 56*x^3/3! + 404*x^4/4! + 3272*x^5/5! +...
where
A(x) = 1/((1-x)^2*(1-x^2/2!)^4*(1-x^3/3!)^8*(1-x^4/4!)^16*(1-x^5/5!)^32*...).
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[1/(1 - x^k/k!)^(2^k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 21 2019 *)
PROG
(PARI) {a(n)=n!*polcoeff(prod(k=1, n, 1/(1-x^k/k!+x*O(x^n))^(2^k)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 09 2011
STATUS
approved