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A140520 a(n) = binomial(n+9, 9)*5^n. 1
1, 50, 1375, 27500, 446875, 6256250, 78203125, 893750000, 9496093750, 94960937500, 902128906250, 8201171875000, 71760253906250, 607202148437500, 4987731933593750, 39901855468750000, 311733245849609375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

With a different offset, number of n-permutations (n>=9) of 6 objects: t, u, v, z, x, y with repetition allowed, containing exactly nine (9) u's.

Example: a(1)=50 because we have

uuuuuuuuut, uuuuuuuuuv, uuuuuuuuuz, uuuuuuuuux, uuuuuuuuuy,

uuuuuuuutu, uuuuuuuuvu, uuuuuuuuzu, uuuuuuuuxu, uuuuuuuuyu,

uuuuuuutuu, uuuuuuuvuu, uuuuuuuzuu, uuuuuuuxuu, uuuuuuuyuu,

uuuuuutuuu, uuuuuuvuuu, uuuuuuzuuu, uuuuuuxuuu, uuuuuuyuuu,

uuuuutuuuu, uuuuuvuuuu, uuuuuzuuuu, uuuuuxuuuu, uuuuuyuuuu,

uuuutuuuuu, uuuuvuuuuu, uuuuzuuuuu, uuuuxuuuuu, uuuuyuuuuu,

uuutuuuuuu, uuuvuuuuuu, uuuzuuuuuu, uuuxuuuuuu, uuuyuuuuuu,

uutuuuuuuu, uuvuuuuuuu, uuzuuuuuuu, uuxuuuuuuu, uuyuuuuuuu,

utuuuuuuuu, uvuuuuuuuu, uzuuuuuuuu, uxuuuuuuuu. uyuuuuuuuu,

tuuuuuuuuu, vuuuuuuuuu, zuuuuuuuuu, xuuuuuuuuu. yuuuuuuuuu.

LINKS

Table of n, a(n) for n=0..16.

FORMULA

From Chai Wah Wu, Mar 20 2017: (Start)

a(n) = 50*a(n-1) - 1125*a(n-2) + 15000*a(n-3) - 131250*a(n-4) + 787500*a(n-5) - 3281250*a(n-6) + 9375000*a(n-7) - 17578125*a(n-8) + 19531250*a(n-9) - 9765625*a(n-10) for n > 9.

G.f.: 1/(1 - 5*x)^10. (End)

MAPLE

seq(binomial(n+9, 9)*5^n, n=0..20);

MATHEMATICA

Table[Binomial[n + 9, 9] 5^n, {n, 0, 16}] (* or *)

CoefficientList[Series[1/(1 - 5 x)^10, {x, 0, 16}], x] (* Michael De Vlieger, Mar 20 2017 *)

PROG

(Sage)[lucas_number2(n, 5, 0)*binomial(n, 9)/5^9 for n in range(9, 26)] # Zerinvary Lajos, Mar 12 2009

CROSSREFS

Sequence in context: A283311 A031602 A231743 * A114251 A004351 A229316

Adjacent sequences:  A140517 A140518 A140519 * A140521 A140522 A140523

KEYWORD

nonn

AUTHOR

Zerinvary Lajos, Jul 02 2008

STATUS

approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)