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A036217 Expansion of 1/(1-3*x)^5; 5-fold convolution of A000244 (powers of 3). 7
1, 15, 135, 945, 5670, 30618, 153090, 721710, 3247695, 14073345, 59108049, 241805655, 967222620, 3794488740, 14635885140, 55616363532, 208561363245, 772903875555, 2833980877035, 10291825290285, 37050571045026 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A027465(n+5,5) (O. Gerard's triangle).

With a different offset, number of n-permutations (n=5) of 4 objects: u, v, z, x with repetition allowed, containing exactly four (4) u's. Example: a(1)=15 because we have uuuuv uuuvu uuvuu uvuuu vuuuu uuuuz uuuzu uuzuu uzuuu zuuuu uuuux uuuxu uuxuu uxuuu xuuuu. - Zerinvary Lajos, Jun 12 2008

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (15,-90,270,-405,243)

FORMULA

a(n) = 3^n*binomial(n+4, 4) = 3^n*A000332(n+4).

G.f. 1/(1-3*x)^5.

MAPLE

seq(binomial(n+4, 4)*3^n, n=0..20); # Zerinvary Lajos, Jun 12 2008

MATHEMATICA

CoefficientList[Series[1/(1-3x)^5, {x, 0, 30}], x] (* Harvey P. Dale, Jun 13 2017 *)

PROG

(Sage) [lucas_number2(n, 3, 0)*binomial(n, 4)/81 for n in range(4, 25)] # Zerinvary Lajos, Mar 10 2009

(MAGMA) [3^n* Binomial(n+4, 4): n in [0..30]]; // Vincenzo Librandi, Oct 14 2011

CROSSREFS

Cf. A000244, A027465.

Sequence in context: A027630 A027629 A023013 * A022643 A125378 A254409

Adjacent sequences:  A036214 A036215 A036216 * A036218 A036219 A036220

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)