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A166896
G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k] * x^n/n ), an integer series in x.
5
1, 1, 2, 6, 16, 45, 142, 459, 1508, 5122, 17787, 62649, 223971, 811339, 2970032, 10974150, 40893393, 153512844, 580082454, 2205046961, 8427087958, 32362949488, 124837337235, 483508287359, 1879669861074, 7332469937755
OFFSET
0,3
FORMULA
G.f.: exp( Sum_{n>=1} A166897(n)*x^n/n ) where A166897(n) = Sum_{k=0..[n/2]} C(n-k,k)^3*n/(n-k).
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 16*x^4 + 45*x^5 + 142*x^6 + 459*x^7 +...
log(A(x)) = x + 3*x^2/2 + 13*x^3/3 + 39*x^4/4 + 126*x^5/5 + 477*x^6/6 + 1765*x^7/7 +...+ A166897(n)*x^n/n +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^3*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)^3*m/(m-k))*x^m/m)+x*O(x^n)), n)}
CROSSREFS
Cf. A166897, variants: A166894, A166898.
Sequence in context: A333070 A290953 A151391 * A148440 A148441 A307606
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 23 2009
STATUS
approved