A177118 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)=5, k=-2 and l=0.

1, 5, 6, 31, 114, 564, 2628, 13211, 66522, 344636, 1804532, 9590028, 51461840, 278821158, 1522272848, 8369233919, 46288773842, 257390692984, 1438037311156, 8068655095524, 45446502511520, 256869804259090, 1456473521972768

Offset

0,2

Links

Table of n, a(n) for n=0..22.

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) -(n-11)*a(n-2) +3*(17*n-56)*a(n-3) -2*(34*n-137)*a(n-4) +24*(n-5)*a(n-5)=0. - R. J. Mathar, Jul 24 2012

Example

a(2)=2*1*5-4=6. a(3)=2*1*6-4+25-2=31. a(4)=2*1*31-4+2*5*6-4=114.

Maple

l:=0: : k := -2 : m:=5: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. A177117.

Sequence in context: A047179 A166023 A137762 * A151506 A122008 A248254

Adjacent sequences: A177115 A177116 A177117 * A177119 A177120 A177121

Keyword

easy,nonn

Author

Richard Choulet, May 03 2010

Status

approved