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A349021
G.f. satisfies A(x) = 1/(1 - x/(1 - x*A(x))^2)^4.
1
1, 4, 18, 104, 671, 4624, 33342, 248412, 1897219, 14774152, 116864936, 936390692, 7584216152, 61992689940, 510728310716, 4236545121924, 35354229533389, 296604036437692, 2500154435955614, 21164005790766980, 179841032283906149, 1533499916749203208
OFFSET
0,2
LINKS
FORMULA
If g.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^s)^t, then a(n) = Sum_{k=0..n} binomial(t*n-(t-1)*(k-1),k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).
MAPLE
A349021 := proc(n)
local s, t ;
s := 2 ;
t := 4;
add( binomial(t*n-(t-1)*(k-1), k) * binomial(n+(s-1)*k-1, n-k) /(n-k+1) , k=0..n) ;
end proc:
seq(A349021(n), n=0..40) ; # R. J. Mathar, May 12 2022
PROG
(PARI) a(n, s=2, t=4) = sum(k=0, n, binomial(t*n-(t-1)*(k-1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 06 2021
STATUS
approved