A199163 E.g.f.: Product_{n>=1} 1/(1 - x^n/n!)^(2^n).
1, 2, 10, 56, 404, 3272, 30688, 316304, 3609656, 44624624, 597131600, 8555752064, 130941724064, 2127005759296, 36577172243776, 663151898857856, 12646212723268576, 252922802230850496, 5294480128736395456, 115747660924409952512, 2638244919080808844544
Offset: 0
Keywords
Examples
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*...).
Crossrefs
Cf. A005651.
Programs
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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 *) -
PARI
{a(n)=n!*polcoeff(prod(k=1, n, 1/(1-x^k/k!+x*O(x^n))^(2^k)), n)}
Formula
a(n) ~ c * n! * n, where c = Product_{k>=2} (1 - 1/k!)^(2^k) = 200.80872040834836274... - Vaclav Kotesovec, Jul 21 2019
Comments