A177169 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=-2.

1, 7, 12, 71, 308, 1752, 9518, 55995, 331024, 2018056, 12445114, 77971468, 493457274, 3154471374, 20324817414, 131901428431, 861253742060, 5654523909972, 37304630338790, 247183333507140, 1644269062695294

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=-2).

Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +5*(-3*n+7)*a(n-2) +2*(26*n-81)*a(n-3) +32*(-n+4)*a(n-4)=0. - R. J. Mathar, Jun 14 2016

Maple

l:=-2: : 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. A177168.

Sequence in context: A358782 A119179 A121983 * A275005 A298678 A219777

Adjacent sequences: A177166 A177167 A177168 * A177170 A177171 A177172

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved