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

Author

Wolfdieter Lang

Keywords

• easy
• nonn

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).

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).

Programs

Magma

[3^n*Binomial(n+6, 6): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011

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 *)

Sage

[3^n*binomial(n+6,6) for n in range(30)] # Zerinvary Lajos, Mar 10 2009

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)