A176751 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=0 and l=-1.

1, 5, 9, 42, 173, 846, 4177, 21691, 114911, 622910, 3428951, 19138401, 108003785, 615344844, 3534413525, 20444816044, 118994823449, 696370777980, 4095034311841, 24185709305851, 143402427296079, 853276282454676

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=0, l=-1).

Conjecture: (n+1)*a(n) +2(1-3n)*a(n-1) +(19-7n)*a(n-2) +4*(8n-25)*a(n-3) +20(4-n)*a(n-4)=0. - R. J. Mathar, Nov 27 2011

Example

a(2)=2*1*5-1=9. a(3)=2*1*9+5^2-1=42. a(4)=2*1*42+2*5*9-1=173.

Maple

l:=-1: : k := 0 : m:=2: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. A176750.

Sequence in context: A271016 A176967 A110421 * A123822 A226065 A321718

Adjacent sequences: A176748 A176749 A176750 * A176752 A176753 A176754

Keyword

easy,nonn

Author

Richard Choulet, Apr 25 2010

Status

approved