A182325 G.f. satisfies: A(x) = ( A(x^2) + x*A(x) )^2.

1, 2, 9, 26, 104, 350, 1321, 4856, 18667, 71870, 282368, 1118470, 4481428, 18093104, 73612825, 301358656, 1240776848, 5133913326, 21337546123, 89037216384, 372879415520, 1566705725194, 6602445412864, 27900407254328, 118197671533743, 501897494200704

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Formula

G.f. satisfies: A(x) = (1 - 2*x*A(x^2) - sqrt(1 - 4*x*A(x^2))) / (2*x^2).

Equals the self-convolution square of A182144, where

a(2*n) = A182144(2*n+1) for n>=0,

a(2*n-1) = A182144(2*n) - a(n) for n>0 with a(0)=1.

a(n) ~ c * d^n / n^(3/2), where d = 4.498712103893737093320276... (same as for A182144), c = 3.2247879599569180737223... . - Vaclav Kotesovec, Aug 08 2014

Example

G.f.: A(x) = 1 + 2*x + 9*x^2 + 26*x^3 + 104*x^4 + 350*x^5 + 1321*x^6 +...
The square-root of the g.f. yields the g.f. of A182144:
A(x)^(1/2) = 1 + x + 4*x^2 + 9*x^3 + 35*x^4 + 104*x^5 + 376*x^6 + 1321*x^7 + 4960*x^8 + 18667*x^9 + 72220*x^10 + 282368*x^11 + 1119791*x^12 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=(subst(A, x, x^2+x*O(x^n))+x*A)^2); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A182144.

Sequence in context: A091469 A125670 A222660 * A008910 A239059 A153977

Adjacent sequences: A182322 A182323 A182324 * A182326 A182327 A182328

Keyword

nonn

Author

Paul D. Hanna, Apr 24 2012

Status

approved