A177122 - OEIS

%I #5 Mar 02 2016 15:26:17

%S 1,6,15,70,325,1721,9449,54208,318943,1918427,11731931,72746099,

%T 456238871,2889149141,18447220199,118630723058,767675233277,

%U 4995186818805,32662752627705,214514289725729,1414397208516269

%N 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.

%F 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).

%F 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

%e 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.

%p 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 :

%p 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);

%Y Cf. A176648.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, May 03 2010