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A004368 Binomial coefficient C(7n,n). 3
1, 7, 91, 1330, 20475, 324632, 5245786, 85900584, 1420494075, 23667689815, 396704524216, 6681687099710, 112992892764570, 1917283000904460, 32626924340528840, 556608279578340080, 9516306085765295355, 163011740982048945441 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..100

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

FORMULA

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

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

From Ilya Gutkovskiy, Jan 16 2017: (Start)

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).

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).

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

MATHEMATICA

Table[Binomial[7n, n], {n, 0, 20}] (* Harvey P. Dale, Apr 05 2014 *)

PROG

(Maxima)

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

taylor(x*diff(B(x), x)/B(x), x, 0, 10); /* Vladimir Kruchinin, Oct 05 2015 */

(PARI) a(n) = binomial(7*n, n) \\ Altug Alkan, Oct 05 2015

(MAGMA) [Binomial(7*n, n): n in [0..20]]; // Vincenzo Librandi, Oct 06 2015

CROSSREFS

Cf. A002296.

Sequence in context: A248226 A165230 A156712 * A243946 A130978 A191097

Adjacent sequences:  A004365 A004366 A004367 * A004369 A004370 A004371

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)