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A036221 Expansion of 1/(1-3*x)^8; 8-fold convolution of A000244 (powers of 3). 3
1, 24, 324, 3240, 26730, 192456, 1250964, 7505784, 42220035, 225173520, 1148384952, 5637526128, 26778249108, 123591918960, 556163635320, 2447119995408, 10553204980197, 44695926974952, 186233029062300 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A027465(n+8,8) (O. Gerard's triangle).

With a different offset, number of n-permutations (n>=7) of 4 objects: u, v, z, x with repetition allowed, containing exactly seven (7) u's. Example: a(1)=24 because we have uuuuuuuv, uuuuuuuz, uuuuuuux, uuuuuuvu, uuuuuuzu, uuuuuuxu, uuuuuvuu, uuuuuzuu, uuuuuxuu, uuuuvuuu, uuuuzuuu, uuuuxuuu, uuuvuuuu, uuuzuuuu, uuuxuuuu, uuvuuuuu, uuzuuuuu, uuxuuuuu, uvuuuuuu, uzuuuuuu, uxuuuuuu, vuuuuuuu, zuuuuuuu, xuuuuuuu. - Zerinvary Lajos, Jun 23 2008

LINKS

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

FORMULA

a(n) = 3^n*binomial(n+7, 7).

G.f.: 1/(1-3*x)^8.

MAPLE

seq(binomial(n+7, 7)*3^n, n=0..18); # Zerinvary Lajos, Jun 23 2008

PROG

(Sage) [lucas_number2(n, 3, 0)*binomial(n, 7)/3^7 for n in range(7, 26)] # Zerinvary Lajos, Mar 13 2009

(MAGMA) [3^n*Binomial(n+7, 7): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011

CROSSREFS

Cf. A000244, A027465.

Sequence in context: A289706 A300846 A006922 * A022652 A292298 A138453

Adjacent sequences:  A036218 A036219 A036220 * A036222 A036223 A036224

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified July 15 23:32 EDT 2020. Contains 335774 sequences. (Running on oeis4.)