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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.
5
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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 23 2009
STATUS
approved