A177131 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)=10, k=0 and l=1.

1, 10, 21, 143, 707, 4716, 29579, 203622, 1399099, 9961582, 71585287, 523465627, 3864076389, 28826865756, 216722056701, 1641392860951, 12507535829603, 95839985593950, 737953189846751, 5707113130311621, 44310704176742745

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=0, l=1).

Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-27*n+59)*a(n-2) +64*(n-3)*a(n-3) +32*(-n+4)*a(n-4)=0. - R. J. Mathar, Jul 24 2012

Example

a(2)=2*1*10+1=21. a(3)=2*1*21+100+1=143.

Maple

l:=1: : k := 0 : m :=10: d(0):=1:d(1):=m: for n from 1 to 28 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, 31); seq(d(n), n=0..29);

Crossrefs

Cf. A177130.

Sequence in context: A121807 A133163 A242831 * A177180 A275248 A041833

Adjacent sequences: A177128 A177129 A177130 * A177132 A177133 A177134

Keyword

easy,nonn

Author

Richard Choulet, May 03 2010

Status

approved