A177197 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)=6, k=-1 and l=1.

1, 6, 11, 56, 241, 1271, 6661, 37006, 208891, 1208821, 7097111, 42266381, 254457091, 1546758771, 9478386011, 58495688356, 363237501841, 2267924619371, 14228919052861, 89660508722431, 567189172324641, 3600736064969121

Offset

0,2

Links

Table of n, a(n) for n=0..21.

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=-1, l=1).

Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(-5*n+19)*a(n-2) +3*(17*n-54)*a(n-3) +60*(-n+4)*a(n-4) +20*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*6-2+1=11. a(3)=2*1*11-2+36-1+1=56.

Maple

l:=1: : k := -1 : m:=6: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. A176967.

Sequence in context: A341943 A271119 A271299 * A177162 A152448 A289285

Adjacent sequences: A177194 A177195 A177196 * A177198 A177199 A177200

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved