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A004368 Binomial coefficient C(7n,n). 3

%I

%S 1,7,91,1330,20475,324632,5245786,85900584,1420494075,23667689815,

%T 396704524216,6681687099710,112992892764570,1917283000904460,

%U 32626924340528840,556608279578340080,9516306085765295355,163011740982048945441

%N Binomial coefficient C(7n,n).

%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.

%H T. D. Noe, <a href="/A004368/b004368.txt">Table of n, a(n) for n = 0..100</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%F a(n) = C(7*n-1,n-1)*C(49*n^2,2)/(3*n*C(7*n+1,3)), n>0. - _Gary Detlefs_, Jan 02 2014

%F G.f.: A(x) = x*B'(x)/B(x), where B(x)+1 is g.f. of A002296. - _Vladimir Kruchinin_, Oct 05 2015

%F From _Ilya Gutkovskiy_, Jan 16 2017: (Start)

%F O.g.f.: 6F5(1/7,2/7,3/7,4/7,5/7,6/7; 1/6,1/3,1/2,2/3,5/6; 823543*x/46656).

%F E.g.f.: 6F6(1/7,2/7,3/7,4/7,5/7,6/7; 1/6,1/3,1/2,2/3,5/6,1; 823543*x/46656).

%F a(n) ~ sqrt(7/3)*7^(7*n)/(2*sqrt(Pi*n)*6^(6*n)). (End)

%t Table[Binomial[7n,n],{n,0,20}] (* _Harvey P. Dale_, Apr 05 2014 *)

%o (Maxima)

%o B(x):=sum(binomial(7*n,n-1)/n*x^n,n,1,30);

%o taylor(x*diff(B(x),x)/B(x),x,0,10); /* _Vladimir Kruchinin_, Oct 05 2015 */

%o (PARI) a(n) = binomial(7*n,n) \\ _Altug Alkan_, Oct 05 2015

%o (MAGMA) [Binomial(7*n,n): n in [0..20]]; // _Vincenzo Librandi_, Oct 06 2015

%Y Cf. A002296.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified February 28 11:08 EST 2020. Contains 332323 sequences. (Running on oeis4.)