A176962 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)=2, k=-1 and l=1.

1, 2, 3, 8, 25, 87, 317, 1190, 4563, 17797, 70399, 281813, 1139659, 4649403, 19112963, 79096156, 329258425, 1377798891, 5792421109, 24454224311, 103631241913, 440674939193, 1879769835969, 8041447249927, 34490981798189

Offset

0,2

Links

Table of n, a(n) for n=0..24.

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) +(11*n-13)*a(n-2) +3*(n-6)*a(n-3) +12*(-n+4)*a(n-4) +4*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*2-2+1=3. a(3)=2*1*3-2+2^2-1+1=8. a(4)=2*1*8-2+2*2*3-2+1=25.

Maple

l:=1: : k := -1 : 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. A176959.

Sequence in context: A277040 A009224 A171199 * A065619 A243963 A111121

Adjacent sequences: A176959 A176960 A176961 * A176963 A176964 A176965

Keyword

easy,nonn

Author

Richard Choulet, Apr 29 2010

Status

approved