A224882 G.f.: 1/(1 - 32*x)^(1/16).

1, 2, 34, 748, 18326, 476476, 12864852, 356540184, 10072260198, 288738125676, 8373405644604, 245112419778408, 7230816383463036, 214699624924363992, 6410317372741724904, 192309521182251747120, 5793324325615333881990, 175162864903898918549580

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = (2^n/n!) * Product_{k=0..n-1} (16*k + 1).

a(n) ~ 32^n/(GAMMA(1/16)*n^(15/16)). - Vaclav Kotesovec, Jul 24 2013

Example

G.f.: A(x) = 1 + 2*x + 34*x^2 + 748*x^3 + 18326*x^4 + 476476*x^5 +...
where
A(x)^16 = 1 + 32*x + 1024*x^2 + 32768*x^3 + 1048576*x^4 +...+ 32^n*x^n +...
Also,
A(x)^8 = 1 + 16*x + 384*x^2 + 10240*x^3 + 286720*x^4 +...+ 8^n*A000984(n)*x^n +...
A(x)^4 = 1 + 8*x + 160*x^2 + 3840*x^3 + 99840*x^4 +...+ 4^n*A004981(n)*x^n +...
A(x)^2 = 1 + 4*x + 72*x^2 + 1632*x^3 + 40800*x^4 +...+ 2^n*A224881(n)*x^n +...

Mathematica

CoefficientList[Series[1/(1-32*x)^(1/16), {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 24 2013 *)

Prog

(PARI) {a(n)=polcoeff(1/(1-32*x +x*O(x^n))^(1/16), n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=(2^n/n!)*prod(k=0, n-1, 16*k + 1)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A224881, A000984, A004981.

Sequence in context: A173208 A344107 A361773 * A227935 A264669 A367510

Adjacent sequences: A224879 A224880 A224881 * A224883 A224884 A224885

Keyword

nonn

Author

Paul D. Hanna, Jul 23 2013

Status

approved