A176857 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)=3, k=-1 and l=0.

1, 3, 4, 14, 48, 191, 776, 3271, 14062, 61601, 273796, 1232248, 5604252, 25718825, 118949392, 553888342, 2594626912, 12218698001, 57812767484, 274701432034, 1310257145600, 6271273757973, 30110943889096, 144992416476339

Offset

0,2

Links

Table of n, a(n) for n=0..23.

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=0).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(7*n-5)*a(n-2) +(19*n-68)*a(n-3) +2*(-16*n+65)*a(n-4) +12*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 01 2016

Example

a(2)=2*1*3-2=4. a(3)=2*1*4-2+3^2-1=14. a(4)=2*1*14-2+2*3*4-2=48.

Maple

l:=0: : k := -1 : m:=3: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. A176856.

Sequence in context: A117718 A268700 A349001 * A356463 A248152 A173735

Adjacent sequences: A176854 A176855 A176856 * A176858 A176859 A176860

Keyword

easy,nonn

Author

Richard Choulet, Apr 27 2010

Status

approved