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A226045 G.f.: ( Sum_{n>=0} (2*n+x)^n * x^n / (1 + 2*n*x + x^2)^n )^(1/2). 0
1, 1, 6, 44, 430, 5162, 72890, 1178978, 21449704, 433116488, 9606793874, 232145293502, 6070097785376, 170763070370848, 5142963967765530, 165115679014587758, 5629558857460143814, 203146937778126705662, 7735490130309647256862 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

Self-convolution yields A187746.

Sum_{k=0..n} a(n)*a(n-k) = (2*n^2 + 2*n + 1) * 2^(n-2) * (n-1)! for n>1.

EXAMPLE

G.f.: A(x) = 1 + x + 6*x^2 + 44*x^3 + 430*x^4 + 5162*x^5 +...

where the square of the g.f. begins

A(x)^2 = 1 + 2*x + 13*x^2 + 100*x^3 + 984*x^4 + 11712*x^5 + 163200*x^6 +...+ A187746(n)*x^n +...

and equals the series

A(x)^2 = 1 + (2+x)*x/(1+2*x+x^2) + (4+x)^2*x^2/(1+4*x+x^2)^2 + (6+x)^3*x^3/(1+6*x+x^2)^3 + (8+x)^4*x^4/(1+8*x+x^2)^4 + (10+x)^5*x^5/(1+10*x+x^2)^5 +...

PROG

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

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Sequence in context: A203159 A279085 A124996 * A001852 A284218 A295978

Adjacent sequences:  A226042 A226043 A226044 * A226046 A226047 A226048

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 24 2013

STATUS

approved

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Last modified July 13 04:01 EDT 2020. Contains 335673 sequences. (Running on oeis4.)