A166898 G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^4 * x^k] * x^n/n ), an integer series in x.

1, 1, 2, 10, 38, 137, 646, 3241, 15623, 79439, 427562, 2317396, 12715372, 71543343, 408543758, 2353591560, 13717994046, 80827739181, 480016288156, 2871701561720, 17304832805996, 104933348346951, 639814473417775

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

G.f.: exp( Sum_{n>=1} A166899(n)*x^n/n ) where A166899(n) = Sum_{k=0..[n/2]} C(n-k,k)^4*n/(n-k).

Example

G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 38*x^4 + 137*x^5 + 646*x^6 + 3241*x^7 +...
log(A(x)) = x + 3*x^2/2 + 25*x^3/3 + 111*x^4/4 + 456*x^5/5 + 2697*x^6/6 + 15961*x^7/7 +...+ A166899(n)*x^n/n +...

Prog

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

Crossrefs

Cf. A166897, variants: A166894, A166898.

Sequence in context: A081956 A056182 A120278 * A143960 A122117 A322211

Adjacent sequences: A166895 A166896 A166897 * A166899 A166900 A166901

Keyword

nonn

Author

Paul D. Hanna, Nov 23 2009

Status

approved