A172362 a(n) = binomial(n+10, 10)*3^n.

1, 33, 594, 7722, 81081, 729729, 5837832, 42532776, 287096238, 1818276174, 10909657044, 62482581252, 343654196886, 1824010737318, 9380626649064, 46903133245320, 228652774570935, 1089463220014455, 5084161693400790

Offset: 0

Author

Zerinvary Lajos, Feb 01 2010

Keywords

• nonn
• easy

Comments

With a different offset, number of n-permutations (n>=10) of 4 objects: u, v, z, x with repetition allowed, containing exactly ten, (10) u's.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (33,-495,4455,-26730,112266,-336798,721710,-1082565,1082565,-649539,177147).

Crossrefs

Cf. A027472, A036216, A036217, A036219, A036220, A036221, A036222, A036223.

Programs

Magma

[3^n*Binomial(n+10, 10): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011

Maple

seq(binomial(n+10, 10)*3^n, n=0..30);

Mathematica

Table[Binomial[n + 10, 10]*3^n, {n, 0, 20}]

Formula

G.f.: 1/(1-3*x)^11. - Vincenzo Librandi, Oct 15 2011

From Amiram Eldar, Aug 28 2022: (Start)

Sum_{n>=0} 1/a(n) = 261617/42 - 15360*log(3/2).

Sum_{n>=0} (-1)^n/a(n) = 7864320*log(4/3) - 47510881/21. (End)