A124384 O.g.f.: A(x) = Sum_{n>=0} x^n*Product_{k=0..n} (1 + 2^k*x).

1, 2, 4, 10, 30, 110, 494, 2734, 18734, 159278, 1685550, 22268974, 367653934, 7597868078, 196929315886, 6402998805550, 261393582040110, 13416320169124910, 865576139256079406, 70227589169019724846, 7172766017169503134766, 921829147482582383174702

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: (G(0) - 1)/(x-1) where G(k) = 1 - (1+x*2^k)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 16 2013

a(n) = Sum_{k=0..floor((n+1)/2)} q-binomial(n-k+1,k)*2^binomial(k,2), where q-binomial is triangle A022166, that is, with q=2. - Vladimir Kruchinin, Jan 21 2020

Example

A(x) = (1+x) + x*(1+x)*(1+2x) + x^2*(1+x)*(1+2x)*(1+4x) + x^3*(1+x)*(1+2x)*(1+4x)*(1+8x) +...

Prog

(PARI) a(n)=polcoeff(sum(k=0, n, x^k*prod(j=0, k, 1+2^j*x+x*O(x^n))), n)

Crossrefs

Cf. A022166.

Sequence in context: A317280 A173940 A101901 * A280432 A001647 A007177

Adjacent sequences: A124381 A124382 A124383 * A124385 A124386 A124387

Keyword

nonn

Author

Paul D. Hanna, Oct 28 2006

Status

approved