A157314 G.f.: A(x) = exp( Sum_{n>=1} A157313(n)*x^n/n ) = 1/Product_{n>=1} (1 - A157313(n-1)*x^n).

1, 1, 2, 5, 16, 62, 298, 1700, 11448, 88622, 778532, 7636888, 82782697, 981775224, 12643542295, 175638751080, 2617558335383, 41650633309937, 704712768652527, 12632584581030449, 239150363847113653, 4767657035201958150

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 62*x^5 + 298*x^6 +...
where the exponential:
A(x) = exp(x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 216*x^5/5 + 1326*x^6/6 +...)
and the product:
1/A(x) = (1 - x)(1 - x^2)(1 - 3*x^3)(1 - 10*x^4)(1 - 43*x^5)(1 - 216*x^6)*...
generate A(x) using the same coefficients (after initial term):
A157313=[1,1,3,10,43,216,1326,9283,74667,672085,6730098,74031079,...].

Crossrefs

Cf. A157313, A157312.

Sequence in context: A138549 A210667 A144188 * A374073 A159603 A058117

Adjacent sequences: A157311 A157312 A157313 * A157315 A157316 A157317

Keyword

nonn

Author

Paul D. Hanna, Mar 10 2009

Status

approved