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A372109
G.f. A(x) satisfies A(x) = ( (1 - x*A(x))/(1 - 5*x*A(x)) )^(1/2).
0
1, 2, 12, 90, 758, 6850, 64904, 636250, 6399120, 65661250, 684665828, 7233956250, 77278356246, 833291781250, 9057750917944, 99144375156250, 1091857567068742, 12089416175781250, 134501879883249300, 1502857085910156250, 16857310306553767026
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} 4^k * binomial(n/2+k-1/2,k) * binomial(n-1,n-k).
PROG
(PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2+k-1/2, k)*binomial(n-1, n-k))/(n+1);
CROSSREFS
Cf. A372090.
Sequence in context: A121357 A098926 A074610 * A250130 A225573 A354233
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 19 2024
STATUS
approved