|
|
A368966
|
|
Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x-x^3)^2 ).
|
|
8
|
|
|
1, 3, 15, 93, 644, 4769, 36953, 295867, 2428373, 20322566, 172759032, 1487632887, 12948891408, 113748663495, 1007117650350, 8978151790011, 80519598139947, 725976573163011, 6576546244337046, 59829384514916820, 546375444906314661, 5006934930385254672
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(4*n-2*k+2,n-3*k).
|
|
PROG
|
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x-x^3)^2)/x)
(PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|