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A172362 a(n) = binomial(n+10, 10)*3^n. 11
1, 33, 594, 7722, 81081, 729729, 5837832, 42532776, 287096238, 1818276174, 10909657044, 62482581252, 343654196886, 1824010737318, 9380626649064, 46903133245320, 228652774570935, 1089463220014455, 5084161693400790 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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
Index entries for linear recurrences with constant coefficients, signature (33,-495,4455,-26730,112266,-336798,721710,-1082565,1082565,-649539,177147).
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)
MAPLE
seq(binomial(n+10, 10)*3^n, n=0..30);
MATHEMATICA
Table[Binomial[n + 10, 10]*3^n, {n, 0, 20}]
PROG
(Magma) [3^n*Binomial(n+10, 10): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011
CROSSREFS
Sequence in context: A228256 A197361 A282926 * A080597 A076684 A181382
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Feb 01 2010
STATUS
approved

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Last modified February 26 03:53 EST 2024. Contains 370335 sequences. (Running on oeis4.)