A206850 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, k^2) * x^k ).

1, 1, 2, 4, 8, 56, 522, 5972, 424954, 16560881, 1528544877, 483389731955, 70609119680761, 53933819677734187, 58734216507052608587, 38789122414735365076327, 202547156817505166242299130, 712808848212730366850407506134, 2914935606380176735260119042755221

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: A359877 A068620 A073953 * A094333 A018473 A004094

Adjacent sequences: A206847 A206848 A206849 * A206851 A206852 A206853

Keyword

nonn

Author

Paul D. Hanna, Feb 13 2012

Status

approved