login
This site is supported by donations to The OEIS Foundation.

 

Logo

The submissions stack has been unacceptably high for several months now. Please voluntarily restrict your submissions and please help with the editing. (We don't want to have to impose further limits.)

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A206850 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, k^2) * x^k ). 9
1, 1, 2, 4, 8, 56, 522, 5972, 424954, 16560881, 1528544877, 483389731955, 70609119680761, 53933819677734187, 58734216507052608587, 38789122414735365076327, 202547156817505166242299130, 712808848212730366850407506134, 2914935606380176735260119042755221 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equals antidiagonal sums of triangle A228902.

LINKS

Table of n, a(n) for n=0..18.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 8*x^4 + 56*x^5 + 522*x^6 + 5972*x^7 +...

such that, by definition, the logarithm equals the series:

log(A(x)) = x*(1+x) + x^2*(1 + 4*x + x^2)/2

+ x^3*(1 + 9*x + 126*x^2 + x^3)/3

+ x^4*(1 + 16*x + 1820*x^2 + 11440*x^3 + x^4)/4

+ x^5*(1 + 25*x + 12650*x^2 + 2042975*x^3 + 2042975*x^4 + x^5)/5

+ x^6*(1 + 36*x + 58905*x^2 + 94143280*x^3 + 7307872110*x^4 + 600805296*x^5 + x^6)/6

+ x^7*(1 + 49*x + 211876*x^2 + 2054455634*x^3 + 3348108992991*x^4 + 63205303218876*x^5 + 262596783764*x^6 + x^7)/7 +...

+ x^n*(Sum_{k=0..n} binomial(n^2, k^2)*x^k)/n  +...

PROG

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

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A206851 (log), A228902, A206830, A167006.

Sequence in context: A018446 A068620 A073953 * A094333 A018473 A004094

Adjacent sequences:  A206847 A206848 A206849 * A206851 A206852 A206853

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 13 2012

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified August 28 10:51 EDT 2015. Contains 261120 sequences.