A176609 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=0 and l=1.

1, 5, 11, 48, 207, 1016, 5159, 27337, 148489, 824232, 4650657, 26602827, 153900879, 898909266, 5293577451, 31395570786, 187364023083, 1124308178270, 6779554362911, 41059231942321, 249646266800185, 1523286825246798

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=0, l=1).

Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-7*n+19)*a(n-2) +24*(n-3)*a(n-3) +12*(-n+4)*a(n-4)=0. - R. J. Mathar, Mar 01 2016

Example

a(2)=2*1*5+1=11. a(3)=2*1*11+5^2+1=48.

Maple

l:=1: : k := 0 : m :=5: 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. A176604, A176605, A176606, A176607.

Sequence in context: A327494 A097743 A350648 * A041213 A142238 A370769

Adjacent sequences: A176606 A176607 A176608 * A176610 A176611 A176612

Keyword

easy,nonn

Author

Richard Choulet, Apr 21 2010

Status

approved