A367071 G.f. satisfies A(x) = 1 + 2*x + 2*x^2*A(x)^2.

1, 2, 2, 8, 16, 48, 136, 384, 1184, 3520, 10944, 34048, 107008, 340480, 1087104, 3502080, 11333120, 36867072, 120491008, 395276288, 1301700608, 4300414976, 14250496000, 47353233408, 157747462144, 526740717568, 1762653863936, 5910312910848

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: A(x) = 2*(1+2*x) / (1+sqrt(1-8*x^2*(1+2*x))).

a(n) = Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(k+1,n-2*k) * A000108(k).

D-finite with recurrence (n+2)*a(n) +8*(-n+1)*a(n-2) +8*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Dec 04 2023

Maple

A367071 := proc(n)
    add(2^(n-k) * binomial(k+1, n-2*k) * A000108(k), k=0..floor(n/2)) ;
end proc:
seq(A367071(n), n=0..70) ; # R. J. Mathar, Dec 04 2023

Prog

(PARI) a(n) = sum(k=0, n\2, 2^(n-k)*binomial(k+1, n-2*k)*binomial(2*k, k)/(k+1));

Crossrefs

Cf. A000108, A253918, A354733.

Sequence in context: A220589 A109190 A016120 * A188115 A085542 A239682

Adjacent sequences: A367068 A367069 A367070 * A367072 A367073 A367074

Keyword

nonn

Author

Seiichi Manyama, Nov 05 2023

Status

approved