|
| |
|
|
A370187
|
|
Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x+x^3)^2 )^n.
|
|
3
|
|
|
|
1, 4, 28, 226, 1940, 17214, 155914, 1432106, 13289076, 124276528, 1169346298, 11057293526, 104986087178, 1000248093420, 9557756114130, 91559051752596, 879027678226452, 8455595252761536, 81476137225450096, 786286875175380088, 7598503022428758570
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(4*n-k,n-3*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / ((1+x)^2 * (1+x+x^3)^2) ). See A369485.
|
|
|
PROG
|
(PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
