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A004368
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Binomial coefficient C(7n,n).
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12
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1, 7, 91, 1330, 20475, 324632, 5245786, 85900584, 1420494075, 23667689815, 396704524216, 6681687099710, 112992892764570, 1917283000904460, 32626924340528840, 556608279578340080, 9516306085765295355, 163011740982048945441
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OFFSET
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0,2
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REFERENCES
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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.
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LINKS
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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].
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FORMULA
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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
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)
The o.g.f. A(x) is algebraic: (1 - A(x))*(1 + 6*A(x))^6 + (7^7)*x*A(x)^7 = 0.
Sum_{n >= 1} a(n)*( x*(6*x + 7)^6/(7^7*(1 + x)^7) )^n = x. (End)
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MATHEMATICA
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PROG
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(Maxima)
B(x):=sum(binomial(7*n, n-1)/n*x^n, n, 1, 30);
(PARI) a(n) = binomial(7*n, n) \\ Altug Alkan, Oct 05 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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