A177125 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)=9, k=1 and l=1.

1, 9, 21, 127, 637, 4007, 24821, 164659, 1106197, 7642295, 53521277, 380565539, 2735155565, 19854481655, 145295269157, 1070969265539, 7943300521541, 59241248227575, 443987081678157, 3342101935397795, 25256877059336861

Offset: 0

Author

Richard Choulet, May 03 2010

Keywords

• easy
• nonn

Examples

			a(2)=2*1*9+2+1=21. a(3)=2*1*21+2+81+1+1=127.
		

Crossrefs

Cf. A177124.

Programs

Maple

l:=1: : k := 1 : m :=9: d(0):=1:d(1):=m: for n from 1 to 32 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, 34); seq(d(n), n=0..32);

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) +(-17*n+43)*a(n-2) +(71*n-214)*a(n-3) +72*(-n+4)*a(n-4) +24*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016