A177122 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)=6, k=1 and l=1.

1, 6, 15, 70, 325, 1721, 9449, 54208, 318943, 1918427, 11731931, 72746099, 456238871, 2889149141, 18447220199, 118630723058, 767675233277, 4995186818805, 32662752627705, 214514289725729, 1414397208516269

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) +(-5*n+19)*a(n-2) +(35*n-106)*a(n-3) +36*(-n+4)*a(n-4) +12*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*6+2+1=15. a(3)=2*1*15+2+36+1+1=70. a(4)=2*1*70+2+2*6*15+2+1=325.

Maple

l:=1: : k := 1 : m :=6: 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);

Crossrefs

Cf. A176648.

Sequence in context: A359923 A035077 A032164 * A108540 A232170 A165570

Adjacent sequences: A177119 A177120 A177121 * A177123 A177124 A177125

Keyword

easy,nonn

Author

Richard Choulet, May 03 2010

Status

approved