cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A227468 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^3, n^2*k) * x^k ).

Original entry on oeis.org

1, 1, 2, 37, 1562313, 122131737394518, 26010968765974205465787541, 22347536974721066092798325076069521074882, 113454243067016764816945424312979214671918840299656114590507, 897202601035299299315214220213621062686601174611936477408260666612934393100592315294994
Offset: 0

Views

Author

Paul D. Hanna, Aug 24 2013

Keywords

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.

Examples

			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 + ...

Crossrefs

Cf. A158110, A206830, A227467.

Programs

  • 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), ", "))

A260756 G.f.: exp( Sum_{n>=1} 2^(n^n) * x^n/n ).

Original entry on oeis.org

1, 2, 10, 44739260, 28948022309329048855892746252171976963317496166410141009864396001978371888518
Offset: 0

Views

Author

Paul D. Hanna, Jul 30 2015

Keywords

Comments

Does the g.f. describe an integer sequence?
The number of digits in the terms begin: [1, 1, 2, 8, 77, 941, 14045, 247911, ...].

Examples

			G.f.: A(x) = 1 + 2*x + 10*x^2 + 44739260*x^3 +...
where
log(A(x)) = 2^1*x + 2^4*x^2/2 + 2^27*x^3/3 + 2^256*x^4/4 + 2^3125*x^5/5 + 2^46656*x^6/6 + 2^823543*x^7/7 + 2^16777216*x^8/8 +...+ 2^(n^n)*x^n/n +...

Crossrefs

Cf. A155200, A158110.

Programs

  • PARI
    {a(n)=polcoeff(exp(sum(m=1, n+1, 2^(m^m)*x^m/m)+x*O(x^n)), n)}
for(n=0,7,print1(a(n),", "))
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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