A202482 Expansion of (1-(1-9*x)^(1/3))/(4-(1-9*x)^(1/3)).

1, 2, 10, 59, 385, 2672, 19336, 144218, 1100530, 8549888, 67386652, 537437222, 4328934754, 35162809688, 287688325672, 2368563539171, 19608128003473, 163116600371846, 1362822870625762, 11430476370562259

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Formula

a(n):=1/n*sum(i=1..n, i*sum(k=0..n-i, binomial(k,n-k-i)*3^(k)*(-1)^(n-k+1)*binomial(n+k-1,n-1))).

Recurrence: 7*(n-1)*n*a(n) = (n-1)*(125*n - 252)*a(n-1) - 9*(61*n^2 - 309*n + 388)*a(n-2) - 9*(3*n-8)*(3*n-7)*a(n-3). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 9^n/(16*Gamma(2/3)*n^(4/3)). - Vaclav Kotesovec, Oct 20 2012

Mathematica

CoefficientList[Series[(1/x) (1- (1 - 9 x)^(1/3)) / (4 - (1 - 9 x)^(1/3)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)
Module[{c=Surd[1-9x, 3]}, Rest[CoefficientList[Series[(1-c)/(4-c), {x, 0, 20}], x]]] (* Harvey P. Dale, Feb 10 2019 *)

Prog

(Maxima)
a(n):=sum(i*sum(binomial(k, n-k-i)*3^(k)*(-1)^(n-k+1)*binomial(n+k-1, n-1), k, 0, n-i), i, 1, n)/n;

Crossrefs

Sequence in context: A262910 A370281 A351502 * A240605 A095993 A029725

Adjacent sequences: A202479 A202480 A202481 * A202483 A202484 A202485

Keyword

nonn

Author

Vladimir Kruchinin, Dec 20 2011

Extensions

Typo in Mathematica code fixed by Vincenzo Librandi, Jun 04 2013

Status

approved