|
|
A307903
|
|
Coefficient of x^n in (1 + n*x + n*x^3)^n.
|
|
2
|
|
|
1, 1, 4, 36, 448, 6875, 124956, 2624293, 62537728, 1667191653, 49158400000, 1588285928306, 55796298391296, 2117279603738494, 86299754734693696, 3760031421065559375, 174374733095888748544, 8575617145497637681301, 445758339115421869936896, 24417549315693295193935516
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..floor(n/3)} n^(n-2*k) * binomial(n,3*k) * binomial(3*k,k).
a(n) ~ exp(3*n^(1/3)/2^(2/3)) * n^(n - 1/6) / (2^(2/3)*sqrt(3*Pi)) * (1 - 79/(36 * 2^(1/3) * n^(1/3))). - Vaclav Kotesovec, May 05 2019
|
|
MATHEMATICA
|
Flatten[{1, Table[n^n * HypergeometricPFQ[{1/3 - n/3, 2/3 - n/3, -n/3}, {1/2, 1}, -27/(4*n^2)], {n, 1, 20}]}] (* Vaclav Kotesovec, May 05 2019 *)
|
|
PROG
|
(PARI) {a(n) = polcoef((1+n*x+n*x^3)^n, n)}
(PARI) {a(n) = sum(k=0, n\3, n^(n-2*k)*binomial(n, 3*k)*binomial(3*k, k))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|