login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001421 (6*n)!/((n!)^3*(3*n)!). 5
1, 120, 83160, 81681600, 93699005400, 117386113965120, 155667030019300800, 214804163196079142400, 305240072216678400087000, 443655767845074392936328000, 656486312795713480715743268160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Self-convolution of A092870, where A092870(n) = (12^n/n!^2) * Product_{k=0..n-1} (12k+1)*(12k+5). - Paul D. Hanna, Jan 25 2011

REFERENCES

M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998. (See Eq. 31.)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..75

R. S. Maier, Nonlinear differential equations satisfied by certain classical modular forms, p. 34 equation (7.29b)

FORMULA

o.g.f.: Hypergeometric2F1(5/12, 1/12; 1; 1728x)^2. - Jacob Lewis (jacobml(AT)uw.edu), Jul 28 2009

a(n) = C(2n,n) * (12^n/n!^2) * Product_{k=0..n-1} (6k+1)*(6k+5). - Paul D. Hanna, Jan 25 2011

G.f.: A(x) = 1 + 120*x + 83160*x^2 + 81681600*x^3 +...  - Paul D. Hanna, Jan 25 2011

A(x)^(1/2) = 1 + 60*x + 39780*x^2 + 38454000*x^3 +...+ A092870(n)*x^n +... - Paul D. Hanna, Jan 25 2011

G.f.: F(1/6, 1/2, 5/6; 1, 1; 1728*x), a hypergeometric series. - Michael Somos, Feb 28 2011

0 = y^3*z^3 - 360*y^4*z^2 + 43200*y^5*z - 1728000*y^6 - 16632*x*y^2*z^3 + 7691328*x*y^3*z^2 - 1738520064*x*y^4*z + 176027074560*x*y^5 + 92207808*x^2*y*z^3 - 69176553984*x^2*y^2*z^2 + 23624298528768*x^2*y^3*z - 2853152143441920*x^2*y^4 - 170400029184*x^3*z^3 + 224945232150528*x^3*y*z^2 - 92759146352345088*x^3*y^2*z + 11686511179538104320*x^3*y^3 where x = a(n), y = a(n+1), z = a(n+2) for all n in z. - Michael Somos, Sep 21 2014

MAPLE

f := n->(6*n)!/( (n!)^3*(3*n)!);

MATHEMATICA

Factorial[6 n]/(Factorial[3n] Factorial[n]^3) (* Jacob Lewis (jacobml(AT)uw.edu), Jul 28 2009 *)

a[ n_] := SeriesCoefficient[ HypergeometricPFQ[ {1/6, 1/2, 5/6}, {1, 1}, 1728 x], {x, 0, n}] (* Michael Somos, Jul 11 2011 *)

PROG

(PARI) {a(n)=(2*n)!/n!^2*(12^n/n!^2)*prod(k=0, n-1, (6*k+1)*(6*k+5))} \\ Paul D. Hanna, Jan 25 2011

(MAGMA) [Factorial(6*n)/(Factorial(n)^3*Factorial(3*n)): n in [0..15]]; // Vincenzo Librandi, Oct 26 2011

CROSSREFS

Cf. A092870; variants: A184423, A008977, A184892, A184896, A184898. - Paul D. Hanna, Jan 25 2011

Sequence in context: A074653 A065961 A058528 * A107446 A184887 A159735

Adjacent sequences:  A001418 A001419 A001420 * A001422 A001423 A001424

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, KUPK78A(AT)prodigy.com (Glenn K Painter)

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 6 11:07 EST 2016. Contains 278776 sequences.