A179533 Expansion of (1/(1-x-2x^2))*c(x/(1-x-2x^2)), c(x) the g.f. of A000108.

1, 2, 7, 23, 85, 332, 1369, 5870, 25945, 117374, 540805, 2528675, 11966923, 57206972, 275824159, 1339721519, 6549093013, 32195473406, 159065828029, 789395034701, 3933239089903, 19668745466636, 98679891233803, 496570499905832, 2505670304785615, 12675395921692394, 64270076976110203, 326580624341708693, 1662796531746045157, 8481930651824392268, 43341418581113085697

Offset

0,2

Comments

Hankel transform is A168495(n+1).

Links

Table of n, a(n) for n=0..30.

Formula

G.f.: 1/(1-x-2x^2-x/(1-x/(1-x-2x^2-x/(1-x/(1-x-2x^2-x/(1-x/(1-x-2x^2-x/(1-x/(1-... (continued fraction);

a(n) = Sum_{k=0..n} A000108(k)*Sum_{j=0..n-k} C(k+j,k)*C(j,n-k-j)*2^(n-k-j).

a(n) = Sum_{k=0..n} A073370(n,k)*A000108(k).

D-finite with recurrence: (n+1)*a(n) +2*(1-3n)*a(n-1) +(n-1)*a(n-2) +4*(3n-5)*a(n-3) +4*(n-3)*a(n-4)= 0. - R. J. Mathar, Nov 17 2011

Maple

with(LREtools): with(FormalPowerSeries): # requires Maple 2022
ogf:= (1/(1-x-2*x^2))*(1 - sqrt(1 - 4*(x/(1-x-2*x^2)))) / (2*(x/(1-x-2*x^2))):
init:= [1, 2, 7, 23, 85, 332, 1369];
iseq:= seq(u(i-1)=init[i], i=1..nops(init)): req:= FindRE(ogf, x, u(n));
rmin:= subs(n=n-4, MinimalRecurrence(req, u(n), {iseq})[1]); # Mathar's recurrence
a:= gfun:-rectoproc({rmin, iseq}, u(n), remember):
seq(a(n), n=0..30); # Georg Fischer, Nov 04 2022

Crossrefs

Cf. A000108, A073370, A168495.

Sequence in context: A150336 A173519 A151292 * A352173 A150337 A150338

Adjacent sequences: A179530 A179531 A179532 * A179534 A179535 A179536

Keyword

nonn

Author

Paul Barry, Jan 08 2011

Status

approved