A176832 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=-1.

1, 5, 11, 49, 211, 1037, 5267, 27953, 152075, 845709, 4780923, 27402033, 158842179, 929655949, 5485858531, 32603081969, 194973609467, 1172405681165, 7084340575307, 42994921155441, 261963852143283, 1601804565028621

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=-1).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(-n+11)*a(n-2) +(31*n-98)*a(n-3) +4*(-10*n+41)*a(n-4) +16*(n-5)*a(n-5)=0. - R. J. Mathar, Feb 18 2016

Example

a(2)=2*1*5+2-1=11. a(3)=2*1*11+2+5^2+1-1=49. a(4)=2*1*49+2+2*5*11+2-1=211.

Maple

l:=-1: : 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. A176830.

Sequence in context: A149519 A149520 A073415 * A289284 A149521 A149522

Adjacent sequences: A176829 A176830 A176831 * A176833 A176834 A176835

Keyword

easy,nonn

Author

Richard Choulet, Apr 27 2010

Status

approved