A162479 Expansion of 1/((1-x)*sqrt(1-4x/(1-x)^4)).

1, 3, 17, 105, 671, 4393, 29249, 197117, 1340579, 9182013, 63247587, 437684991, 3040564703, 21191554941, 148109893057, 1037660903785, 7285259590495, 51244141331581, 361046057274899, 2547558161041995, 17999651555835001

Offset: 0

Author

Paul Barry, Jul 04 2009

Keywords

• easy
• nonn

Comments

Partial sums are A162480. Partial sums of A162478.

Formula

G.f.: 1/(1-x-2x/((1-x)^3-x/(1-x-x/((1-x)^3-x/(1-x-x/((1-x)^3-x/(1-... (continued fraction);

a(n)=sum{k=0..n, C(n+3k,n-k)*A000984(k)}.

Conjecture D-finite with recurrence: n*a(n) +3*(2-3n)*a(n-1) +2*(7n-13)*a(n-2)+2*(12-5n)*a(n-3) +(5n-16)*a(n-4) +(4-n)*a(n-5)=0. - R. J. Mathar, Nov 17 2011