A176856 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=0.

1, 2, 2, 5, 14, 47, 164, 590, 2156, 7985, 29900, 113054, 431132, 1656641, 6408776, 24942227, 97596698, 383740409, 1515431648, 6008307998, 23907184340, 95439446687, 382146649616, 1534364232089, 6176307411014, 24919973908607

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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=0).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(11*n-13)*a(n-2) +(7*n-32)*a(n-3) +2*(-10*n+41)*a(n-4) +8*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 01 2016

Example

a(2)=2*1*2-2=2. a(3)=2*1*2-2+2^2-1=5. a(4)=2*1*5-2+2*2*2-2=14.

Maple

l:=0: : 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. A176855.

Sequence in context: A208201 A185966 A032097 * A112709 A291573 A208353

Adjacent sequences: A176853 A176854 A176855 * A176857 A176858 A176859

Keyword

easy,nonn

Author

Richard Choulet, Apr 27 2010

Status

approved