A206848 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, k^2) ).

1, 2, 5, 53, 3422, 826606, 1335470713, 9548109569885, 190076214495558260, 18558289189760778318731, 10286810587274357297985552184, 16301371794177939084545371104827679, 91249944361047494534207504939405352235731, 3283593155431496336538359592977826684908598341441

Offset

0,2

Comments

Logarithmic derivative yields A206849.

Equals row sums of triangle A228902.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..57

Example

G.f.: A(x) = 1 + 2*x + 5*x^2 + 53*x^3 + 3422*x^4 + 826606*x^5 + 1335470713*x^6 +...
where the logarithm of the g.f. yields the l.g.f. of A206849:
log(A(x)) = 2*x + 6*x^2/2 + 137*x^3/3 + 13278*x^4/4 + 4098627*x^5/5 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m^2, k^2))*x^m/m)+x*O(x^n)), n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A206849 (log), A206846, A206850, A228902.

Cf. variants: A167006, A228809.

Sequence in context: A330282 A071880 A071882 * A081482 A134475 A218030

Adjacent sequences: A206845 A206846 A206847 * A206849 A206850 A206851

Keyword

nonn

Author

Paul D. Hanna, Feb 15 2012

Status

approved