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A208977 Self-convolution square-root of A005810, where A005810(n) = binomial(4*n,n). 0
1, 2, 12, 86, 666, 5388, 44832, 380424, 3275172, 28512248, 250413856, 2215112886, 19711078686, 176276723508, 1583186541144, 14271487891512, 129063176166570, 1170480053359908, 10641805703955624, 96970507481607972, 885397365149468076, 8098908925136867112 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

G.f.: A(x) = sqrt( G(x)/(4 - 3*G(x)) ) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293. [From a formula by Mark van Hoeij in A005810]

EXAMPLE

G.f.: A(x) = 1 + 2*x + 12*x^2 + 86*x^3 + 666*x^4 + 5388*x^5 +...

The square of the g.f. equals the g.f. of A005810:

A(x)^2 = 1 + 4*x + 28*x^2 + 220*x^3 + 1820*x^4 + 15504*x^5 +...

The g.f. of A002293 is G(x) = 1 + x*G(x)^4:

G(x) = 1 + x + 4*x^2 + 22*x^3 + 140*x^4 + 969*x^5 + 7084*x^6 +...

PROG

(PARI) {a(n)=polcoeff(sum(k=0, n, binomial(4*k, k)*x^k +x*O(x^n))^(1/2), n)}

for(n=0, 41, print1(a(n), ", "))

CROSSREFS

Cf. A005810, A002293.

Sequence in context: A052867 A226238 A179495 * A097237 A055531 A181345

Adjacent sequences:  A208974 A208975 A208976 * A208978 A208979 A208980

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 03 2012

STATUS

approved

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Last modified December 7 19:05 EST 2016. Contains 278895 sequences.