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A141054 Binomial(n+8,8)*8^n and 8-idempotent numbers. example: A059300 Triangle of idempotent numbers binomial(n,k)*k^(n-k), version 4. A059300 formatted as a triangular array: 1 72 ........... 6
1, 72, 2880, 84480, 2027520, 42172416, 787218432, 13495173120, 215922769920, 3262832967680, 46984794734592, 649244436332544, 8656592484433920, 111869810568069120, 1406363332855726080, 17251390216363573248 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

COMMENTS

With a different offset, number of n-permutations of 9 objects:

p, r, s, t, u, v, z, x, y with repetition allowed, containing exactly eight (8) u's. Example: a(1)=72 because we have

uuuuuuuup, uuuuuuupu, uuuuuupuu, uuuuupuuu, uuuupuuuu, uuupuuuuu, uupuuuuuu, upuuuuuuu, puuuuuuuu,

uuuuuuuur, uuuuuuuru, uuuuuuruu, uuuuuruuu, uuuuruuuu, uuuruuuuu, uuruuuuuu, uruuuuuuu, ruuuuuuuu,

uuuuuuuus, uuuuuuusu, uuuuuusuu, uuuuusuuu, uuuusuuuu, uuusuuuuu, uusuuuuuu, usuuuuuuu, suuuuuuuu,

uuuuuuuut, uuuuuuutu, uuuuuutuu, uuuuutuuu, uuuutuuuu, uuutuuuuu, uutuuuuuu, utuuuuuuu, tuuuuuuuu,

uuuuuuuuv, uuuuuuuvu, uuuuuuvuu, uuuuuvuuu, uuuuvuuuu, uuuvuuuuu, uuvuuuuuu, uvuuuuuuu, vuuuuuuuu,

uuuuuuuuz, uuuuuuuzu, uuuuuuzuu, uuuuuzuuu, uuuuzuuuu, uuuzuuuuu, uuzuuuuuu, uzuuuuuuu, zuuuuuuuu,

uuuuuuuux, uuuuuuuxu, uuuuuuxuu, uuuuuxuuu, uuuuxuuuu, uuuxuuuuu, uuxuuuuuu, uxuuuuuuu, xuuuuuuuu,

uuuuuuuuy, uuuuuuuyu, uuuuuuyuu, uuuuuyuuu, uuuuyuuuu, uuuyuuuuu, uuyuuuuuu, uyuuuuuuu, yuuuuuuuu.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..400

FORMULA

a(n)=C(n+8,8)*8^n.

G.f.: 1/(1-8*x)^9. - Vincenzo Librandi, Oct 16 2011

MAPLE

seq(binomial(n+8, 8)*8^n, n=0..17);

PROG

(MAGMA) [8^n* Binomial(n+8, 8): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011

CROSSREFS

Cf. A000027, A001788, A036216, A040075, A050982, A050988, A050989, A059297, A059300, .

Sequence in context: A035731 A035803 A017735 * A173192 A004366 A004389

Adjacent sequences:  A141051 A141052 A141053 * A141055 A141056 A141057

KEYWORD

nonn,easy

AUTHOR

Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 01 2008

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Last modified February 17 09:17 EST 2012. Contains 206009 sequences.