The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A169959 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A169959

a(n) = binomial(10*n, n).
(history; published version)

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

PROG

(MAGMAMagma) [Binomial(10*n, n): n in [0..50]]; // Vincenzo Librandi, Apr 21 2011

Discussion

Thu Sep 08

08:45

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

#29 by Michael De Vlieger at Mon Feb 21 10:51:17 EST 2022

STATUS

reviewed

approved

#28 by Joerg Arndt at Mon Feb 21 10:32:12 EST 2022

STATUS

proposed

reviewed

#27 by Michel Marcus at Mon Feb 21 06:12:54 EST 2022

STATUS

editing

proposed

#26 by Michel Marcus at Mon Feb 21 06:12:52 EST 2022

FORMULA

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

STATUS

proposed

editing

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

STATUS

editing

proposed

#24 by Peter Bala at Mon Feb 21 05:39:49 EST 2022

CROSSREFS

binomial(k*n,n): A000984 (k = 2), A005809 (k = 3), A005810 (k = 4), A001449 (k = 5), A004355 (k = 6), A004368 (k = 7), A004381 (k = 8), A169958 - A169961 (k = 10 9 thru 12).

#23 by Peter Bala at Mon Feb 21 05:30:41 EST 2022

FORMULA

From Peter Bala, Feb 21 2022: (Start)

The o.g.f. A(x) is algebraic: (1 - A(x))*(1 + 9*A(x))^9 + (10^10)*x*A(x)^10 = 0.

Sum_{n >= 1} a(n)*( x*(9*x + 10)^9/(10^10*(1 + x)^10) )^n = x. (End)

CROSSREFS

binomial(k*n,n): A000984 (k = 2), A005809 (k = 3), A005810 (k = 4), A001449 (k = 5), A004355 (k = 6), A004368 (k = 7), A004381 (k = 8), A169958 - A169961 (k = 10 thru 12).

STATUS

approved

editing

#22 by N. J. A. Sloane at Sun Jan 19 11:28:53 EST 2020

FORMULA

From Peter Bala, Jan 17 2020: (Start)

a(n) = Sum_{k = 0..n} (k + 1)*binomial(10*n-k-2, n-k).

a(n) = Sum_{k = 0..n} (-1)^(n+k)*binomial(n*(x+9), k)*binomial(n*x-k-1, n-k), for arbitrary x. (End)

KEYWORD

nonn,changed

nonn

STATUS

proposed

approved

#21 by Peter Bala at Sun Jan 19 07:49:01 EST 2020

STATUS

editing

proposed