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A372035
G.f. A(x) satisfies A(x) = ( 1 + 4*x*A(x)/(1 - x) )^(1/2).
1
1, 2, 4, 6, 6, 2, -4, -2, 20, 50, 24, -130, -302, -14, 1176, 2166, -874, -10494, -15464, 15886, 95006, 107586, -210624, -860234, -686084, 2499602, 7733116, 3460038, -27992190, -68487790, -3894404, 301924750, 592203732, -243714366, -3165123736, -4936196082
OFFSET
0,2
FORMULA
G.f.: A(x) = (1-x)/(-2*x + sqrt(1-2*x+5*x^2)).
a(n) = Sum_{k=0..n} 4^k * binomial(k/2+1/2,k) * binomial(n-1,n-k)/(k+1).
a(n) = 2 * A371888(n) for n > 0.
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec((1-x)/(-2*x+sqrt(1-2*x+5*x^2)))
(PARI) a(n) = sum(k=0, n, 4^k*binomial(k/2+1/2, k)*binomial(n-1, n-k)/(k+1));
CROSSREFS
Sequence in context: A141765 A234574 A010587 * A213473 A134920 A011031
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 16 2024
STATUS
approved