

A177131


Sequence defined by the recurrence formula a(n+1)=sum(a(p)*a(np)+k,p=0..n)+l for n>=1, with here a(0)=1, a(1)=10, k=0 and l=1.


0



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

0,2


LINKS

Table of n, a(n) for n=0..20.


FORMULA

G.f f: f(z)=(1sqrt(14*z*(a(0)z*a(0)^2+z*a(1)+(k+l)*z^2/(1z)+k*z^2/(1z)^2)))/(2*z) (k=0, l=1).
Conjecture: (n+1)*a(n) +2*(3*n+1)*a(n1) +(27*n+59)*a(n2) +64*(n3)*a(n3) +32*(n+4)*a(n4)=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(np)+k, p=0..n)+l:od :
taylor((1sqrt(14*z*(d(0)z*d(0)^2+z*m+(k+l)*z^2/(1z)+k*z^2/(1z)^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



