A177163 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)=7, k=0 and l=-1.

1, 7, 13, 74, 329, 1862, 10253, 60603, 361851, 2222538, 13829307, 87365033, 557739245, 3595994096, 23371254161, 152986926652, 1007633073829, 6673187517652, 44409186387853, 296827429782051, 1991755355228811

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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=0, l=-1).

Conjecture: +(n+1)*a(n) +2*(-3*n+1)*a(n-1) +5*(-3*n+7)*a(n-2) +4*(12*n-37)*a(n-3) +28*(-n+4)*a(n-4)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*7-1=13. a(3)=2*1*13+49-1=74.

Maple

l:=-1: : k := 0 : m:=7: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. A177162.

Sequence in context: A098478 A174878 A177198 * A268350 A061521 A362246

Adjacent sequences: A177160 A177161 A177162 * A177164 A177165 A177166

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved