A196560 G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^4 * x^k]^2 * x^n/n ).

1, 1, 3, 20, 205, 2624, 24793, 283522, 3639005, 50426826, 740744940, 10801827249, 163698355616, 2554965416964, 40878247859612, 667841855292388, 11051724909284834, 185702751266940874, 3162454792706586691, 54508849210857505845

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 20*x^3 + 205*x^4 + 2624*x^5 + 24793*x^6 +...
where
log(A(x)) = (1 + x)^2*x + (1+2^4*x+x^2)^2*x^2/2 + (1+3^4*x+3^4*x^2+x^3)^2*x^3/3 + (1+4^4*x+6^4*x^2+4^4*x^3+x^4)^2*x^4/4 +...
More explicitly,
log(A(x)) = x + 5*x^2/2 + 52*x^3/3 + 733*x^4/4 + 11926*x^5/5 + 129944*x^6/6 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^4*x^k)^2*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A166898, A180718, A196559.

Sequence in context: A367922 A052590 A081209 * A257476 A218673 A230478

Adjacent sequences: A196557 A196558 A196559 * A196561 A196562 A196563

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2011

Status

approved