A259272 L.g.f.: log(G(x)/x) where G(x) is the g.f. of A259270.

4, 64, 1264, 28064, 675504, 17304544, 466669536, 13155395904, 385761948592, 11725112136544, 368418702111904, 11942661856743104, 398739401015768544, 13694120483326491328, 483240865665765964224, 17505677353238744717952, 650483549418017027126704, 24776136706182576128200288

Offset

1,1

Comments

G.f. G(x) of A259270 satisfies: G( x - 2*G(x)*H(x) ) = x, where H'(x) = 2*G(x).

Links

Paul D. Hanna, Table of n, a(n) for n = 1..199

Example

L.g.f.: L(x) = 4*x^2/2 + 64*x^4/4 + 1264*x^6/6 + 28064*x^8/8 + 675504*x^10/10 +...
where the g.f. of A259270 begins:
G(x) = x*exp(L(x)) = x + 2*x^3 + 18*x^5 + 244*x^7 + 4090*x^9 + 78636*x^11 +...+ A259270(n)*x^(2*n-1) +...
Now let H(x) = Integral G(x) dx, then
L(x) = 2*G(x)*H(x)/x + [d/dx 4*G(x)^2*H(x)^2/x]/2! + [d^2/dx^2 8*G(x)^3*H(x)^3/x]/3! + [d^3/dx^3 16*G(x)^4*H(x)^4/x]/4! + [d^4/dx^4 32*G(x)^5*H(x)^5/x]/5! +...

Prog

(PARI) {a(n)=local(A=x+x*O(x^n), B=x^2); for(i=1, n, B=intformal(2*A); A = serreverse(x - 2*A*B +O(x^(2*n+2)))); 2*n*polcoeff(log(A/x), 2*n)}
for(n=1, 25, print1(a(n), ", "))

Crossrefs

Cf. A259270, A259271.

Sequence in context: A085807 A014729 A322519 * A361963 A085532 A371661

Adjacent sequences: A259269 A259270 A259271 * A259273 A259274 A259275

Keyword

nonn

Author

Paul D. Hanna, Jun 29 2015

Status

approved