OFFSET
0,3
COMMENTS
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
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..381 (terms 1..100 from Vincenzo Librandi)
FORMULA
a(n) = n^(n/2)*GegenbauerPoly(n,-n,-sqrt(n)/2). - Emanuele Munarini, Oct 20 2016
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
MAPLE
seq(n!*coeff(series(exp(n*x)*BesselI(0, 2*sqrt(n)*x), x, n+1), x, n), n=1..17);
MATHEMATICA
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,
12}] (* Emanuele Munarini, Oct 20 2016 *)
PROG
(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);
makelist(a(n), n, 1, 12); /* Emanuele Munarini, Mar 02 2011 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Perry, Mar 19 2004
EXTENSIONS
a(0)=1 prepended by Seiichi Manyama, May 01 2019
STATUS
approved