A098565 Numbers that appear as binomial coefficients exactly 6 times.

120, 210, 1540, 7140, 11628, 24310, 61218182743304701891431482520

Offset: 1

Author

Paul D. Hanna, Oct 27 2004

Keywords

• nonn
• more

Links

• Jean-Marie de Koninck, Nicolas Doyon, and William Verreault, Repetitions of multinomial coefficients and a generalization of Singmaster's conjecture, arXiv:2107.09107 [math.NT], 2021.
• Zoe Griffiths, My MegaFavNumber: 61,218,182,743,304,701,891,431,482,520, YouTube video, 2020.
• David Singmaster, How Often Does An Integer Occur As A Binomial Coefficient?, American Mathematical Monthly, 78(4), 1971, pp. 385-386; also on Fermat's Library.
• Wikipedia, Singmaster's conjecture
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

See A098564 for more information.

Cf. A185024, A182237. Subsequence of A003015.

Cf. A059233.

Programs

Haskell

import Data.List (elemIndices)
a098565 n = a098565_list !! (n-1)
a098565_list = map (+ 2 ) $ elemIndices 3 a059233_list
-- Reinhard Zumkeller, Dec 24 2012

Formula

A059233(a(n)) = 3. - Reinhard Zumkeller, Dec 24 2012

Extensions

a(7) from T. D. Noe, Jul 13 2005