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A134095
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E.g.f.: A(x) = 1/(1 - LambertW(-x)^2 ).
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2
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1, 0, 2, 12, 120, 1480, 22320, 396564, 8118656, 188185680, 4871980800, 139342178140, 4363291266048, 148470651659928, 5455056815237120, 215238256785814500, 9077047768435752960, 407449611073696325536
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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.
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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 (vladeta(AT)eunet.rs), Oct 17 2007
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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 ).
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MAPLE
| seq(simplify(GAMMA(n+1, -n)*(-exp(-1))^n), n=0..20); - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 17 2007
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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)=local(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)}
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CROSSREFS
| Cf. A060435; indirectly related: A062817, A132608.
Cf. A063170.
Sequence in context: A127112 A003580 A052580 * A204042 A189981 A052680
Adjacent sequences: A134092 A134093 A134094 * A134096 A134097 A134098
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 11 2007
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