A036219 Expansion of 1/(1-3*x)^6; 6-fold convolution of A000244 (powers of 3).

1, 18, 189, 1512, 10206, 61236, 336798, 1732104, 8444007, 39405366, 177324147, 773778096, 3288556908, 13660159464, 55616363532, 222465454128, 875957725629, 3400777052442, 13036312034361, 49400761393368, 185252855225130, 688082033693340, 2533392942234570

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (18,-135,540,-1215,1458,-729).

Formula

a(n) = 3^n*binomial(n+5, 5).

a(n) = A027465(n+6, 6).

G.f.: 1/(1-3*x)^6.

E.g.f.: (1/40)*(40 + 600*x + 1800*x^2 + 1800*x^3 + 675*x^4 + 81*x^5)*exp(3*x). - G. C. Greubel, May 19 2021

From Amiram Eldar, Sep 22 2022: (Start)

Sum_{n>=0} 1/a(n) = 240*log(3/2) - 385/4.

Sum_{n>=0} (-1)^n/a(n) = 3840*log(4/3) - 4415/4. (End)

Maple

seq(3^n*binomial(n+5, 5), n=0..30); # Zerinvary Lajos, Jun 13 2008

Mathematica

Table[3^n*Binomial[n+5, 5], {n, 0, 30}] (* G. C. Greubel, May 19 2021 *)
CoefficientList[Series[1/(1-3x)^6, {x, 0, 30}], x] (* or *) LinearRecurrence[ {18, -135, 540, -1215, 1458, -729}, {1, 18, 189, 1512, 10206, 61236}, 30] (* Harvey P. Dale, Jan 02 2022 *)

Prog

(Sage) [3^n*binomial(n+5, 5) for n in range(30)] # Zerinvary Lajos, Mar 10 2009
(Magma) [3^n*Binomial(n+5, 5): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011

Crossrefs

Cf. A027465.

Sequences of the form 3^n*binomial(n+m, m): A000244 (m=0), A027471 (m=1), A027472 (m=2), A036216 (m=3), A036217 (m=4), this sequence (m=5), A036220 (m=6), A036221 (m=7), A036222 (m=8), A036223 (m=9), A172362 (m=10).

Sequence in context: A341393 A023016 A073385 * A022646 A268447 A259163

Adjacent sequences: A036216 A036217 A036218 * A036220 A036221 A036222

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved