A176967 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=-1 and l=1.

1, 5, 9, 41, 169, 825, 4073, 21113, 111657, 603961, 3317353, 18472697, 104002729, 591135417, 3387188969, 19545660025, 113483969833, 662493218361, 3886235869033, 22895917401593, 135419375707561, 803779534739897

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) +(-n+11)*a(n-2) +3*(13*n-42)*a(n-3) +48*(-n+4)*a(n-4) +16*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*5-2+1=9. a(3)=2*1*9-2+5^2-1+1=41. a(4)=2*1*41-2+2*5*9-2+1=169.

Maple

l:=1: : k := -1 : 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. A176966.

Sequence in context: A270673 A269702 A271016 * A110421 A176751 A123822

Adjacent sequences: A176964 A176965 A176966 * A176968 A176969 A176970

Keyword

easy,nonn

Author

Richard Choulet, Apr 29 2010

Status

approved