A036220 Expansion of 1/(1-3*x)^7; 7-fold convolution of A000244 (powers of 3).

1, 21, 252, 2268, 17010, 112266, 673596, 3752892, 19702683, 98513415, 472864392, 2192371272, 9865670724, 43257171636, 185387878440, 778629089448, 3211844993973, 13036312034361, 52145248137444, 205836505805700, 802762372642230, 3096369151620030

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (21,-189,945,-2835,5103,-5103,2187).

Formula

a(n) = 3^n*binomial(n+6, 6).

a(n) = A027465(n+7,7).

G.f.: 1/(1-3*x)^7.

E.g.f.: (1/80)*(80 + 1440*x + 5400*x^2 + 7200*x^3 + 4050*x^4 + 972*x^5 + 81*x^6)*exp(3*x). - G. C. Greubel, May 19 2021

From Amiram Eldar, Sep 22 2022: (Start)

Sum_{n>=0} 1/a(n) = 1173/5 - 576*log(3/2).

Sum_{n>=0} (-1)^n/a(n) = 18432*log(4/3) - 26508/5. (End)

Maple

seq(3^n*binomial(n+6, 6), n=0..20); # Zerinvary Lajos, Jun 16 2008

Mathematica

Table[3^n*Binomial[n+6, 6], {n, 0, 30}] (* G. C. Greubel, May 19 2021 *)

Prog

(Sage) [3^n*binomial(n+6, 6) for n in range(30)] # Zerinvary Lajos, Mar 10 2009
(Magma) [3^n*Binomial(n+6, 6): 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), A036219 (m=5), this sequence (m=6), A036221 (m=7), A036222 (m=8), A036223 (m=9), A172362 (m=10).

Sequence in context: A165108 A282923 A023019 * A022649 A165094 A365849

Adjacent sequences: A036217 A036218 A036219 * A036221 A036222 A036223

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved