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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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6
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1, 8, 81, 1120, 19375, 400896, 9630411, 262955008, 8032730715, 271175200000, 10017828457483, 401738097475584, 17371952344599385, 805429080795852800, 39844314853048828125, 2094272851244149112832, 116526044312704751752451
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also coefficient of X^n in expansion of (1-2*n*X+(n^2-4*n)*X^2)^(-1/2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 22 2004
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..100
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FORMULA
| Sum_{k=floor(n/2)..n} n^k*binomial(n, k)*binomial(k, n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 22 2004
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MAPLE
| 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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PROG
| (PARI) q(n)=(1+n*X+n*X^2)^n; for(i=1, 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);
makelist(a(n), n, 1, 12); /* Emanuele Munarini, Mar 02 2011 */
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CROSSREFS
| Sequence in context: A068617 A007778 A065440 * A022519 A138439 A193563
Adjacent sequences: A092363 A092364 A092365 * A092367 A092368 A092369
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KEYWORD
| nonn
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AUTHOR
| Jon Perry (perry(AT)globalnet.co.uk), Mar 19 2004
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