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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

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 | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 23:12 EST 2016. Contains 278900 sequences.