login
A372003
G.f. A(x) satisfies A(x) = ( 1 + 9*x*(1 + x*A(x)) )^(1/3).
4
1, 3, -6, 36, -216, 1404, -9648, 68904, -506304, 3802464, -29055024, 225142416, -1764900576, 13970400480, -111506362560, 896391836928, -7251109424640, 58978357310592, -482049643011840, 3957079727715840, -32609916223598592, 269682253882186752
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} 9^k * binomial(n/3-k/3+1/3,k) * binomial(k,n-k)/(n-k+1).
D-finite with recurrence n*(n-2)*a(n) +3*(8*n^2-31*n+24)*a(n-1) +27*(7*n^2-41*n+56)*a(n-2) +54*(3*n-10)*(3*n-14)*a(n-3) -108*(n-4)*(n-7)*a(n-6) -648*(n-6)*(n-8)*a(n-7)=0. - R. J. Mathar, Apr 22 2024
MAPLE
A372003 := proc(n)
add(9^k*binomial((n-k+1)/3, k)*binomial(k, n-k)/(n-k+1), k=0..n) ;
end proc:
seq(A372003(n), n=0..60) ; # R. J. Mathar, Apr 22 2024
PROG
(PARI) a(n) = sum(k=0, n, 9^k*binomial(n/3-k/3+1/3, k)*binomial(k, n-k)/(n-k+1));
CROSSREFS
Cf. A372002.
Sequence in context: A003674 A211895 A240986 * A120595 A048642 A264702
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 15 2024
STATUS
approved