A177183 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)=8, k=-1 and l=-1.

1, 8, 13, 86, 375, 2289, 12807, 79376, 487669, 3112659, 20011341, 131002051, 865156193, 5775171729, 38841026305, 263161175842, 1793749636759, 12294401226021, 84671929129311, 585688412266001, 4067110924673259

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=-1, l=-1).

Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(-13*n+35)*a(n-2) +(83*n-262)*a(n-3) +4*(-25*n+101)*a(n-4) +36*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*8-2-1=13. a(3)=2*1*13-2+64-1-1=86.

Maple

l:=-1: : k := -1 : m:=8: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. A177182.

Sequence in context: A166670 A107764 A306131 * A228799 A329499 A220393

Adjacent sequences: A177180 A177181 A177182 * A177184 A177185 A177186

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved