A180473 Expansion of o.g.f. x*s(x)/(1-x*s(x)-x^2*s(x)^2), where s(x) is the o.g.f. of the little Schroeder numbers (A001003).

1, 2, 7, 27, 114, 509, 2365, 11318, 55411, 276231, 1397430, 7156089, 37023225, 193229466, 1016141199, 5378940051, 28638955098, 153267403397, 824014568581, 4448456379134, 24104579252971, 131055735586767, 714741620026542, 3908997981612017, 21434123083817329

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

a(n) = Sum_{k=1..n} (k/(2^k*n))*(Sum_{j=0..n-k} binomial(n,j)*2^(n-j)*(-1)^j*binomial(2*n-k-j-1, n-1))*Fibonacci(k).

Prog

(Maxima) a(n):=sum(k/(2^k*n)*sum(binomial(n, j)*2^(n-j)*(-1)^j*binomial(2*n-k-j-1, n-1), j, 0, n-k)*fib(k), k, 1, n);
(PARI) seq(n)={my(p=x*(1+x-sqrt(1 - 6*x + x^2 + O(x*x^n)))/(4*x)); Vec(p/(1 - p - p^2))} \\ Andrew Howroyd, Apr 17 2021

Crossrefs

Sequence in context: A150628 A106225 A127897 * A011965 A154108 A150629

Adjacent sequences: A180470 A180471 A180472 * A180474 A180475 A180476

Keyword

nonn

Author

Vladimir Kruchinin, Sep 07 2010

Extensions

Terms a(21) and beyond from Andrew Howroyd, Apr 17 2021

Status

approved