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

0,2

Comments

Compare to the e.g.f. of A005651 (sum of multinomial coefficients): Product_{n>=1} 1/(1 - x^n/n!).

Links

Table of n, a(n) for n=0..20.

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

Cf. A005651.

Sequence in context: A336961 A265954 A093303 * A303830 A235321 A364306

Adjacent sequences: A199160 A199161 A199162 * A199164 A199165 A199166

Keyword

nonn

Author

Paul D. Hanna, Nov 09 2011

Status

approved