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A245496 a(n) = n! * [x^n] (exp(x)+x)^n. 4
1, 2, 10, 87, 1096, 18045, 365796, 8793337, 244327616, 7701562377, 271493172100, 10582453248741, 451909972458000, 20980984760560045, 1052197311966267572, 56683993296812515425, 3264626390205804733696, 200168726219982496336401, 13017989155680578824221060 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of ways to place n labeled balls (colored red and blue) into n labeled bins so that if a blue ball occupies a bin then there are no other balls with it. - Geoffrey Critzer, Jan 30 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) ~ (1+exp(-1))^(n+1/2) * n^n.

E.g.f.: 1 / ((1 - x) * (1 + LambertW(-x/(1 - x)))). - Ilya Gutkovskiy, Jan 25 2020

MATHEMATICA

Table[n!*SeriesCoefficient[(E^x+x)^n, {x, 0, n}], {n, 0, 20}]

Flatten[{1, Table[n!+Sum[Binomial[n, j]^2*(n-j)^(n-j)*j!, {j, 0, n-1}], {n, 1, 20}]}]

PROG

(PARI) seq(n)={Vec(serlaplace(1/((1 - x) * (1 + lambertw(-x/(1 - x) + O(x*x^n))))), -(n+1))} \\ Andrew Howroyd, Jan 25 2020

CROSSREFS

Cf. A231797, A245493, A245405.

Sequence in context: A208833 A145082 A295836 * A185388 A245009 A306404

Adjacent sequences:  A245493 A245494 A245495 * A245497 A245498 A245499

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jul 24 2014

STATUS

approved

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Last modified February 26 12:43 EST 2020. Contains 332280 sequences. (Running on oeis4.)