|
|
A307905
|
|
Coefficient of x^n in (1 + n*x + x^3)^n.
|
|
3
|
|
|
1, 1, 4, 30, 304, 3875, 59631, 1076383, 22309120, 522262245, 13631508400, 392535959156, 12362973152751, 422774554883590, 15600699362473876, 617888566413340503, 26145122799198386944, 1177107512023013681429, 56185125998674634494980, 2834081165961033246374350
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..floor(n/3)} n^(n-3*k) * binomial(n,3*k) * binomial(3*k,k).
a(n) ~ c * n^n, where c = Sum_{k>=0} 1/(k!*(2*k)!) = HypergeometricPFQ[{}, {1/2, 1}, 1/4] = 1.52106585051363080966025715155941607334728986626976774617... - Vaclav Kotesovec, May 05 2019
|
|
MAPLE
|
f:= n -> coeff((1+n*x+x^3)^n, x, n):
|
|
MATHEMATICA
|
Flatten[{1, Table[n^n * HypergeometricPFQ[{1/3 - n/3, 2/3 - n/3, -n/3}, {1/2, 1}, -27/(4*n^3)], {n, 1, 20}]}] (* Vaclav Kotesovec, May 05 2019 *)
|
|
PROG
|
(PARI) {a(n) = polcoef((1+n*x+x^3)^n, n)}
(PARI) {a(n) = sum(k=0, n\3, n^(n-3*k)*binomial(n, 3*k)*binomial(3*k, k))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|