login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A227468 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^3, n^2*k) * x^k ). 0
1, 1, 2, 37, 1562313, 122131737394518, 26010968765974205465787541, 22347536974721066092798325076069521074882, 113454243067016764816945424312979214671918840299656114590507, 897202601035299299315214220213621062686601174611936477408260666612934393100592315294994 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Compare the definition to: exp( Sum_{n>=1} (1+y)^(n^3) * x^n/n ), which yields an integer series whenever y is an integer (e.g., A158110).

Note: exp( Sum_{n>=1} (1+x)^(n^3) * x^n/n ) does not yield an integer series.

LINKS

Table of n, a(n) for n=0..9.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 37*x^3 + 1562313*x^4 + 122131737394518*x^5 + ...

such that the logarithm equals

log(A(x)) = (1+x)*x + (1 + 70*x + x^2)*x^2/2

+ (1 + 4686825*x + 4686825*x^2 + x^3)*x^3/3

+ (1 + 488526937079580*x + 1832624140942590534*x^2 + 488526937079580*x^3 + x^4)*x^/4 + ...

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m^3, m^2*k)*x^k)*x^m/m)+x*O(x^n)), n)}

for(n=0, 15, print1(a(n), ", "))

CROSSREFS

Cf. A158110, A206830, A227467.

Sequence in context: A277409 A201556 A284309 * A049487 A163792 A050899

Adjacent sequences:  A227465 A227466 A227467 * A227469 A227470 A227471

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 24 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 05:37 EDT 2021. Contains 347577 sequences. (Running on oeis4.)