A177127 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)=6, k=0 and l=1.

1, 6, 13, 63, 283, 1492, 8019, 45270, 261219, 1542254, 9251023, 56269627, 346115245, 2149556612, 13459568885, 84879754663, 538612428155, 3436623582022, 22034604531623, 141897138868677, 917376314956897

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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*(-3*n+1)*a(n-1) +(-11*n+27)*a(n-2) +32*(n-3)*a(n-3) +16*(-n+4)*a(n-4)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*6+1=13. a(3)=2*1*13+36+1=63. a(4)=2*1*63+2*6*13+1=283.

Maple

l:=1: : k := 0 : m :=6: d(0):=1:d(1):=m: for n from 1 to 28 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, 31); seq(d(n), n=0..29);

Crossrefs

Cf. A176609.

Sequence in context: A374348 A262238 A111366 * A177175 A301605 A119110

Adjacent sequences: A177124 A177125 A177126 * A177128 A177129 A177130

Keyword

easy,nonn

Author

Richard Choulet, May 03 2010

Status

approved