A176612 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, 7, 22, 77, 297, 1217, 5192, 22807, 102427, 468067, 2169227, 10170687, 48155437, 229916207, 1105682842, 5350944837, 26040130117, 127349649297, 625556921097, 3085016483557, 15268791946687, 75816909660597

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(11*n-13)*a(n-2) +(-13*n+38)*a(n-3) +12*(n-4)*a(n-4) +4*(-n+5)*a(n-5)=0. - R. J. Mathar, Feb 29 2016

Example

a(2)=2*1*2+2+1=7. a(3)=2*1*7+2+2^2+1+1=22. a(4)=2*1*22+2+2*2*7+2+1=77.

Maple

l:=1: : k := 1 : m :=2: d(0):=1:d(1):=m: for n from 1 to 32 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, 34); seq(d(n), n=0..32);

Crossrefs

Cf. A176611.

Sequence in context: A174403 A119975 A106188 * A132838 A047095 A110137

Adjacent sequences: A176609 A176610 A176611 * A176613 A176614 A176615

Keyword

easy,nonn

Author

Richard Choulet, Apr 21 2010

Status

approved