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A322899
a(n) = T_{2*n}(n+1) where T_{n}(x) is a Chebyshev polynomial of the first kind.
2
1, 7, 577, 119071, 46099201, 28860511751, 26650854921601, 34100354867927167, 57780789062419261441, 125283240358674708816199, 338393251269110482793304001, 1114259437504123772777608493087, 4394174409561746573589926449440001
OFFSET
0,2
FORMULA
a(n) = T_{n}(2*n^2+4*n+1).
a(n) = Sum_{k=0..n} binomial(2*n,2*k)*(n^2+2*n)^(n-k)*(n+1)^(2*k).
a(n) ~ exp(2) * 2^(2*n-1) * n^(2*n). - Vaclav Kotesovec, Apr 15 2020
MATHEMATICA
a[n_] := ChebyshevT[2n, n+1];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Jan 02 2019 *)
PROG
(PARI) {a(n) = polchebyshev(2*n, 1, n+1)}
(PARI) {a(n) = sum(k=0, n, binomial(2*n, 2*k)*(n^2+2*n)^(n-k)*(n+1)^(2*k))}
CROSSREFS
Diagonal of A188644.
Sequence in context: A068616 A080810 A153405 * A203680 A261532 A295814
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 30 2018
STATUS
approved