A176859 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=0.

1, 5, 8, 38, 152, 743, 3608, 18515, 96542, 515525, 2792780, 15341492, 85186412, 477531833, 2698428176, 15355638218, 87919098128, 506118923897, 2927616746156, 17007899032118, 99191713057280, 580535666936861

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=0).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(-n+11)*a(n-2) +(43*n-140)*a(n-3) +2*(-28*n+113)*a(n-4) +20*(n-5)*a(n-5)=0. - R. J. Mathar, Feb 21 2016

Example

a(2)=2*1*5-2=8. a(3)=2*1*8-2+5^2-1=38. a(4)=2*1*38-2+2*5*8-2=152.

Maple

l:=0: : 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. A176858.

Sequence in context: A204676 A219947 A075273 * A176757 A280965 A151349

Adjacent sequences: A176856 A176857 A176858 * A176860 A176861 A176862

Keyword

easy,nonn

Author

Richard Choulet, Apr 27 2010

Status

approved