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A176648 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=1 and l=1. 2
1, 5, 13, 55, 245, 1215, 6317, 34187, 190093, 1079983, 6239989, 36554363, 216600357, 1295906671, 7817665373, 47499325915, 290411653437, 1785401003887, 11030252590149, 68444469966843, 426386709191893, 2665740642304879 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

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=1).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(-n+11)*a(n-2) +(23*n-70)*a(n-3) +24*(-n+4)*a(n-4) +8*(n-5)*a(n-5)=0. - R. J. Mathar, Feb 29 2016

EXAMPLE

a(2)=2*1*5+2+1=13. a(3)=2*1*13+2+5^2+1+1=55. a(4)=2*1*55+2+2*5*13+2+1=245.

MAPLE

l:=1: : k := 1 : m :=5: 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 :

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);

CROSSREFS

Cf. A176645, A176612.

Sequence in context: A149546 A149547 A149548 * A159489 A149549 A149550

Adjacent sequences:  A176645 A176646 A176647 * A176649 A176650 A176651

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Apr 22 2010

STATUS

approved

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Last modified May 8 08:29 EDT 2021. Contains 343658 sequences. (Running on oeis4.)