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%I #33 Sep 22 2022 01:54:45
%S 1,21,252,2268,17010,112266,673596,3752892,19702683,98513415,
%T 472864392,2192371272,9865670724,43257171636,185387878440,
%U 778629089448,3211844993973,13036312034361,52145248137444,205836505805700,802762372642230,3096369151620030
%N Expansion of 1/(1-3*x)^7; 7-fold convolution of A000244 (powers of 3).
%H Vincenzo Librandi, <a href="/A036220/b036220.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (21,-189,945,-2835,5103,-5103,2187).
%F a(n) = 3^n*binomial(n+6, 6).
%F a(n) = A027465(n+7,7).
%F G.f.: 1/(1-3*x)^7.
%F 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
%F From _Amiram Eldar_, Sep 22 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 1173/5 - 576*log(3/2).
%F Sum_{n>=0} (-1)^n/a(n) = 18432*log(4/3) - 26508/5. (End)
%p seq(3^n*binomial(n+6,6), n=0..20); # _Zerinvary Lajos_, Jun 16 2008
%t Table[3^n*Binomial[n+6, 6], {n,0,30}] (* _G. C. Greubel_, May 19 2021 *)
%o (Sage) [3^n*binomial(n+6,6) for n in range(30)] # _Zerinvary Lajos_, Mar 10 2009
%o (Magma) [3^n*Binomial(n+6, 6): n in [0..30]]; // _Vincenzo Librandi_, Oct 15 2011
%Y Cf. A027465.
%Y 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).
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
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