The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A169961 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A169961

a(n) = binomial(12*n, n).
(history; published version)

#29 by Charles R Greathouse IV at Thu Sep 08 08:45:49 EDT 2022

PROG

(MAGMAMagma) [Binomial(12*n, n): n in [0..20]]; // Vincenzo Librandi, Aug 07 2014

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#28 by Michael De Vlieger at Mon Feb 21 10:51:10 EST 2022

STATUS

reviewed

approved

#27 by Joerg Arndt at Mon Feb 21 10:32:19 EST 2022

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proposed

reviewed

#26 by Michel Marcus at Mon Feb 21 06:13:59 EST 2022

STATUS

editing

proposed

#25 by Michel Marcus at Mon Feb 21 06:13:41 EST 2022

FORMULA

a(n) = C(12*n-1,n-1)*C(144*n^2,2)/(3*n*C(12*n+1,3)), n>0. - Gary Detlefs, Jan 02 2014

From _Peter Bala, _, Feb 21 2022: (Start)

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proposed

editing

#24 by Peter Bala at Mon Feb 21 05:53:40 EST 2022

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editing

proposed

#23 by Peter Bala at Mon Feb 21 05:44:54 EST 2022

FORMULA

From Peter Bala, Feb 21 2022: (Start)

The o.g.f. A(x) is algebraic: (1 - A(x))*(1 + 11*A(x))^11 + (12^12)*x*A(x)^12 = 0.

Sum_{n >= 1} a(n)*( x*(11*x + 12)^11/(12^12*(1 + x)^12) )^n = x. (End)

STATUS

approved

editing

#22 by Michael Somos at Sun Jul 15 08:02:35 EDT 2018

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proposed

approved

#21 by Vaclav Kotesovec at Sun Jul 15 07:21:19 EDT 2018

STATUS

editing

proposed

#20 by Vaclav Kotesovec at Sun Jul 15 07:20:48 EDT 2018

FORMULA

From Vaclav Kotesovec, Jul 15 2018: (Start)

Recurrence: 11*n*(11*n - 10)*(11*n - 9)*(11*n - 8)*(11*n - 7)*(11*n - 6)*(11*n - 5)*(11*n - 4)*(11*n - 3)*(11*n - 2)*(11*n - 1)*a(n) = 41472*(2*n - 1)*(3*n - 2)*(3*n - 1)*(4*n - 3)*(4*n - 1)*(6*n - 5)*(6*n - 1)*(12*n - 11)*(12*n - 7)*(12*n - 5)*(12*n - 1)*a(n-1).

a(n) ~ 2^(24*n + 1/2) * 3^(12*n + 1/2) / (sqrt(Pi*n) * 11^(11*n + 1/2)). (End)

STATUS

proposed

editing