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A213170 E.g.f.: exp(2*(1-exp(x))). 5
1, -2, 2, 2, -6, -14, 26, 178, 90, -2382, -9446, 13746, 287194, 998578, -3687782, -56264782, -208446118, 1017677490, 17194912282, 79540574642, -317691584294, -7577787031374, -47958156443238, 77252406086578 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Exponential self-convolution of complementary Bell numbers (A000587). - Vladimir Reshetnikov, Oct 07 2016

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..580

Vaclav Kotesovec, Graph - asymptotic (1000 terms)

FORMULA

a(n) = Sum_{k=0..n} A048993(n,k)*(-2)^k.

a(n) = Sum_{k=0..n} A000587(k)*A000587(n-k)*binomial(n,k).

G.f.: 1/(1+2*x/(1-x/(1+2*x/(1-2*x/(1+2*x/(1-3*x/(1+2*x/(1-4*x/(1+2*x/(1-...(continued fraction).

Sum_{k=0..n} binomial(n,k)*a(k) = a(n+1)/(-2). - Philippe Deléham, Feb 17 2013

G.f.: 1/Q(0) where Q(k) = 1 + x*(k+1) + x/(1 - 2*x*(k+1)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 07 2013

Lim sup n->infinity (abs(a(n))/n!)^(1/n) / abs(exp(1/LambertW(-n/2)) / LambertW(-n/2)) = 1. - Vaclav Kotesovec, Aug 04 2014

a(n) = B_n(-2), where B_n(x) is n-th Bell polynomial. - Vladimir Reshetnikov, Oct 20 2015

MATHEMATICA

CoefficientList[Series[E^(2*(1-E^x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Aug 04 2014 *)

Table[BellB[n, -2], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 20 2015 *)

PROG

(PARI) x='x+O('x^50); Vec(serlaplace(exp(2*(1-exp(x))))) \\ G. C. Greubel, Nov 15 2017

CROSSREFS

Cf. A000587, A001861, A007318, A048993.

Sequence in context: A248765 A007039 A025248 * A101416 A098920 A270557

Adjacent sequences:  A213167 A213168 A213169 * A213171 A213172 A213173

KEYWORD

sign,easy

AUTHOR

Philippe Deléham, Feb 14 2013

STATUS

approved

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Last modified November 19 14:52 EST 2018. Contains 317352 sequences. (Running on oeis4.)