A177115 Sequence defined by the recurrence formula a(n+1)=sum(a(p)*a(n-p)+k,p=0..n)+l for n>=1, with here a(0)=1, a(1)=3, k=-2 and l=0.

1, 3, 2, 7, 18, 72, 268, 1075, 4282, 17400, 71116, 293620, 1220752, 5112038, 21537872, 91258183, 388625970, 1662613076, 7142659852, 30802016924, 133292024608, 578640249138, 2519298795680, 10998088033568, 48131763072528

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

G.f f: f(z)=(1-sqrt(1-4*z*(a(0)-z*a(0)^2+z*a(1)+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z) (k=-2, l=0).

Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(7*n-5)*a(n-2) +3*(9*n-32)*a(n-3) +2*(-22*n+89)*a(n-4) +16*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*3-4=2. a(3)=2*1*2-4+3^2-2=7. a(4)=2*1*7-4+2*3*2-4=18.

Maple

l:=0: : k := -2 : m:=3:d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p)+k, p=0..n)+l:od :
taylor((1-sqrt(1-4*z*(d(0)-z*d(0)^2+z*m+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z), z=0, 30); seq(d(n), n=0..30);

Crossrefs

Cf. A177113.

Sequence in context: A049970 A344211 A104528 * A316087 A196537 A173099

Adjacent sequences: A177112 A177113 A177114 * A177116 A177117 A177118

Keyword

easy,nonn

Author

Richard Choulet, May 03 2010

Status

approved