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A199163 E.g.f.: Product_{n>=1} 1/(1 - x^n/n!)^(2^n). 0
1, 2, 10, 56, 404, 3272, 30688, 316304, 3609656, 44624624, 597131600, 8555752064, 130941724064, 2127005759296, 36577172243776, 663151898857856, 12646212723268576, 252922802230850496, 5294480128736395456, 115747660924409952512, 2638244919080808844544 (list; graph; refs; listen; history; text; internal format)
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 A248403

Adjacent sequences:  A199160 A199161 A199162 * A199164 A199165 A199166

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 09 2011

STATUS

approved

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Last modified October 24 10:40 EDT 2021. Contains 348225 sequences. (Running on oeis4.)