A371471 a(n) = binomial(n^2,n) mod n^5.

0, 6, 84, 796, 5, 3792, 7, 27768, 22608, 56440, 11, 83772, 13, 168448, 61065, 471536, 17, 445320, 19, 994080, 2258235, 4188272, 23, 6083208, 156275, 743912, 13548492, 3588928, 29, 16444800, 31, 28887008, 13685133, 2841992, 42053795, 49421088, 37, 24763840, 9171162

Offset: 1

Author

Seiichi Manyama, Mar 24 2024

Keywords

• nonn

References

• D. B. Fuks and Serge Tabachnikov, Mathematical Omnibus: Thirty Lectures on Classic Mathematics, American Mathematical Society, 2007. Lecture 2. Arithmetical Properties of Binomial Coefficients, pages 27-44.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014062, A081369.

Programs

Mathematica

A371471[n_] := Mod[Binomial[n^2, n], n^5];
Array[A371471, 50] (* Paolo Xausa, Jul 28 2025 *)

PARI

a(n) = binomial(n^2, n)%n^5;

Formula

If p is prime and p>=5, a(p) = p.