A177118 - OEIS

A177118

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)=5, k=-2 and l=0.

1, 5, 6, 31, 114, 564, 2628, 13211, 66522, 344636, 1804532, 9590028, 51461840, 278821158, 1522272848, 8369233919, 46288773842, 257390692984, 1438037311156, 8068655095524, 45446502511520, 256869804259090, 1456473521972768, 8282305232312840, 47223174189562544, 269912586111183786

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OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..1276

FORMULA

G.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=-2, l=0).

Conjecture: (n+1)*a(n) -(7*n-2)*a(n-1) -(n-11)*a(n-2) +3*(17*n-56)*a(n-3) -2*(34*n-137)*a(n-4) +24*(n-5)*a(n-5)=0. - R. J. Mathar, Jul 24 2012

Conjecture verified using differential equation 12*z^4 - 35*z^3 + 33*z^2 - 5*z - 1 + (2*z^4 - 15*z^3 + 9*z^2 - 5*z + 1)*f(z) + (24*z^6 - 68*z^5 + 51*z^4 - z^3 - 7*z^2 + z)*f'(z) = 0 satisfied by the g.f. - Robert Israel, Jan 07 2026

EXAMPLE

a(2)=2*1*5-4=6. a(3)=2*1*6-4+25-2=31. a(4)=2*1*31-4+2*5*6-4=114.

MAPLE

l:=0: : k := -2 : m:=5: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. A177117.

Sequence in context: A047179 A166023 A137762 * A151506 A122008 A248254

Adjacent sequences: A177115 A177116 A177117 * A177119 A177120 A177121

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, May 03 2010

STATUS

approved