A176964 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)=3, k=-1 and l=1.

1, 3, 5, 17, 61, 245, 1021, 4405, 19453, 87589, 400541, 1855493, 8689213, 41068965, 195659357, 938623045, 4530198013, 21982331237, 107178047773, 524805028357, 2579684059581, 12724878633765, 62968424313821, 312503657989317

Offset

0,2

Links

Table of n, a(n) for n=0..23.

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) +(7*n-5)*a(n-2) +3*(5*n-18)*a(n-3) +24*(-n+4)*a(n-4) +8*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*3-2+1=5. a(3)=2*1*5-2+3^2-1+1=17. a(4)=2*1*17-2+2*3*5-2+1=61.

Maple

l:=1: : k := -1 : m:=3: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. A176962.

Sequence in context: A049540 A097144 A219108 * A085749 A281623 A350142

Adjacent sequences: A176961 A176962 A176963 * A176965 A176966 A176967

Keyword

easy,nonn

Author

Richard Choulet, Apr 29 2010

Status

approved