A129839 a(n) = Stirling_2(n,3)^2.

0, 0, 0, 1, 36, 625, 8100, 90601, 933156, 9150625, 87048900, 812307001, 7486748676, 68447640625, 622473660900, 5641104760201, 51003678922596, 460438253730625, 4152386009780100, 37422167780506201, 337103845136750916, 3035761307578140625, 27332814735512302500

Offset: 0

Author

N. J. A. Sloane, Feb 08 2008

Keywords

• nonn
• easy

Links

• H. S. Wilf, A lot of toast, with a side order of roast, manuscript, Jan 04 2002.
• Index entries for linear recurrences with constant coefficients, signature (25,-239,1115,-2664,3060,-1296).

Crossrefs

Cf. A000392.

Programs

Mathematica

StirlingS2[Range[0,30],3]^2 (* Harvey P. Dale, Jan 03 2013 *)

PARI

a(n)=(3^n-3<Charles R Greathouse IV, Jan 03 2013

Sage

[stirling_number2(n,3)^2for n in range(0,23)] # Zerinvary Lajos, Mar 14 2009

Formula

G.f.: x^3*(1+11*x-36*x^2-36*x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-6*x)*(1-9*x)).

a(n) = (3^n - 3*2^n + 3)^2/36 for n>0. - Charles R Greathouse IV, Jan 03 2013

Extensions

Definition corrected (exponent changed from 3 to 2) by Harvey P. Dale, Jan 03 2013