A036068 Expansion of (-1+1/(1-3*x)^3)/(9*x).

1, 6, 30, 135, 567, 2268, 8748, 32805, 120285, 433026, 1535274, 5373459, 18600435, 63772920, 216827928, 731794257, 2453663097, 8178876990, 27119434230, 89494132959, 294052151151, 962352494676, 3138105960900, 10198844372925

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

G.f. for a(n)=A027472(n+3), n >= 0, is 1/(1-3*x)^3.

Links

• W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
• Index entries for linear recurrences with constant coefficients, signature (9, -27, 27).

Crossrefs

Cf. A001792, A027472. a(n)= A030524(n+1, 1) (first column of triangle).

Programs

Mathematica

CoefficientList[Series[((1/(1-3x))^3-1)/(9x),{x,0,30}],x] (* Harvey P. Dale, Nov 26 2018 *)

Formula

a(n) = 3^(n-1)*binomial(n+3, 2); G.f.: (-1+(1-3*x)^(-3))/(x*3^2)=(1-3*x+3*x^2)/(1-3*x)^3.

G.f.: F(4,1;2;3x); [From Paul Barry, Sep 03 2008]

D-finite with recurrence: (n+1)*a(n) +3*(-n-3)*a(n-1)=0. - R. J. Mathar, Jan 28 2020