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 A134095 E.g.f.: A(x) = 1/(1 - LambertW(-x)^2). 12
 1, 0, 2, 12, 120, 1480, 22320, 396564, 8118656, 188185680, 4871980800, 139342178140, 4363291266048, 148470651659928, 5455056815237120, 215238256785814500, 9077047768435752960, 407449611073696325536, 19396232794530856894464, 976025303642559490903980 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS E.g.f. equals the square of the e.g.f. of A060435, where A060435(n) = number of functions f: {1,2,...,n} -> {1,2,...,n} with even cycles only. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n) = Sum_{k=0..n} C(n,k) * (n-k)^k * k^(n-k). a(n) = n!*Sum_{k=0..n} (-1)^(n-k)*n^k/k!. - Vladeta Jovovic, Oct 17 2007 a(n) ~ (1/8)*(4*n-1)*n^(n-1). - Vaclav Kotesovec, Nov 27 2012 a(n) = n! * [x^n] exp(n*x)/(1 + x). - Ilya Gutkovskiy, Sep 18 2018 EXAMPLE E.g.f.: A(x) = 1 + 0*x + 2*x^2/2! + 12*x^3/3! + 120*x^4/4! + 1480*x^5/5! + ... The formula A(x) = 1/(1 - LambertW(-x)^2) is illustrated by: A(x) = 1/(1 - (x + x^2 + 3^2*x^3/3! + 4^3*x^4/4! + 5^4*x^5/5! + ...)^2). MAPLE seq(simplify(GAMMA(n+1, -n)*(-exp(-1))^n), n=0..20); # Vladeta Jovovic, Oct 17 2007 MATHEMATICA CoefficientList[Series[1/(1-LambertW[-x]^2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Nov 27 2012 *) a[x0_] := x D[1/x Exp[x], {x, n}] x^n Exp[-x] /. x->x0 Table[a[n], {n, 0, 20}] (* Gerry Martens, May 05 2016 *) PROG (PARI) {a(n)=sum(k=0, n, (n-k)^k*k^(n-k)*binomial(n, k))} (PARI) /* Generated by e.g.f. 1/(1 - LambertW(-x)^2 ): */ {a(n)=my(LambertW=-x*sum(k=0, n, (-x)^k*(k+1)^(k-1)/k!) +x*O(x^n)); n!*polcoeff(1/(1-subst(LambertW, x, -x)^2), n)} CROSSREFS Cf. A060435; indirectly related: A062817, A132608. Cf. A063170, A277458, A277490, A277510. Sequence in context: A127112 A003580 A052580 * A204042 A302702 A189981 Adjacent sequences:  A134092 A134093 A134094 * A134096 A134097 A134098 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 11 2007 STATUS approved

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Last modified August 5 10:38 EDT 2021. Contains 346466 sequences. (Running on oeis4.)