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A092366
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Coefficient of x^n in expansion of (1+n*x+n*x^2)^n.
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12
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1, 1, 8, 81, 1120, 19375, 400896, 9630411, 262955008, 8032730715, 271175200000, 10017828457483, 401738097475584, 17371952344599385, 805429080795852800, 39844314853048828125, 2094272851244149112832, 116526044312704751752451
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OFFSET
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0,3
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COMMENTS
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Also coefficient of x^n in expansion of (1-2*n*x+(n^2-4*n)*x^2)^(-1/2). - Vladeta Jovovic, Mar 22 2004
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LINKS
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FORMULA
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Sum_{k=floor(n/2)..n} n^k*binomial(n, k)*binomial(k, n-k). - Vladeta Jovovic, Mar 22 2004
a(n) ~ n^(n-1/4) * exp(2*sqrt(n)-2) / (2*sqrt(Pi)). - Vaclav Kotesovec, Apr 17 2014
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MAPLE
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seq(n!*coeff(series(exp(n*x)*BesselI(0, 2*sqrt(n)*x), x, n+1), x, n), n=1..17);
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MATHEMATICA
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Table[Sum[n^k*Binomial[n, k]*Binomial[k, n-k], {k, Floor[n/2], n}], {n, 1, 20}] (* Vaclav Kotesovec, Apr 17 2014 *)
Table[If[n == 0, 1, n^(n/2) GegenbauerC[n, -n, -Sqrt[n]/2]], {n, 0,
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PROG
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(PARI) q(n)=(1+n*x+n*x^2)^n; for(i=0, 20, print1(", "polcoeff(q(i), i)))
(Magma) P<x>:=PolynomialRing(Integers()); [ Coefficients((1+n*x+n*x^2)^n)[n+1]: n in [1..22] ]; // Klaus Brockhaus, Mar 03 2011
(Maxima) a(n):=coeff(expand((1+n*x+n*x^2)^n), x, n);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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