A196196 G.f.: A(x) = Sum_{n>=0} x^n*(A(n*x) + A(-n*x))/2.

1, 1, 1, 2, 5, 15, 97, 528, 7525, 81413, 2330257, 53229494, 2883887781, 143434131379, 14268520503521, 1569684574492244, 282300076226827269, 69232924049740233209, 22337274702237239579729, 12261557957001826246975754, 7069170473480519272781373829

Offset

0,4

Links

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

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 97*x^6 + 528*x^7 +...
where
A(x) = 1 + x*(A(x)+A(-x))/2 + x^2*(A(2*x)+A(-2*x))/2 + x^3*(A(3*x)+A(-3*x))/2 + x^4*(A(4*x)+A(-4*x))/2 +...
Related expansions begin:
(A(x)+A(-x))/2 = 1 + x^2 + 5*x^4 + 97*x^6 + 7525*x^8 +...
(A(2*x)+A(-2*x))/2 = 1 + 4*x^2 + 80*x^4 + 6208*x^6 +...
(A(3*x)+A(-3*x))/2 = 1 + 9*x^2 + 405*x^4 + 70713*x^6 +...
(A(4*x)+A(-4*x))/2 = 1 + 16*x^2 + 1280*x^4 + 397312*x^6 +...
(A(5*x)+A(-5*x))/2 = 1 + 25*x^2 + 3125*x^4 + 1515625*x^6 +...
(A(6*x)+A(-6*x))/2 = 1 + 36*x^2 + 6480*x^4 + 4525632*x^6 +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*(subst(A, x, j*x)+subst(A, x, -j*x))/2)); polcoeff(A, n)}

Crossrefs

Cf. A196195, A210525.

Sequence in context: A090140 A032267 A191477 * A266573 A268121 A306794

Adjacent sequences: A196193 A196194 A196195 * A196197 A196198 A196199

Keyword

nonn

Author

Paul D. Hanna, Sep 29 2011

Status

approved