A072867 A Ramanujan congruence modulo 11^2 related to partition numbers: a(n) = p(121*n-5)/121 where p(k) is the k-th partition number.

9825688, 690587635751, 3895157555937180, 5870824778815109405, 3785163537257390979782, 1331088890498177501120122, 295175742637140311468159615, 45387116230097904962420628542, 5170069264521752014176860572055, 457880645545087313878878724639982

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Joseph Lehner, Ramanujan's identities involving the partition function for moduli 11^a, Amer. J. Math., Vol. 65, No. 3 (1943), pp. 492-520.

Formula

a(n) = A000041(121*n - 5)/121.

Mathematica

a[n_] := PartitionsP[121*n - 5]/121; Array[a, 10] (* Amiram Eldar, May 09 2025 *)

Prog

(PARI) a(n) = {numbpart(121*n-5)/121} \\ Andrew Howroyd, Apr 20 2021

Crossrefs

Cf. A000041.

Sequence in context: A234057 A214014 A339478 * A034606 A233839 A059044

Adjacent sequences: A072864 A072865 A072866 * A072868 A072869 A072870

Keyword

nonn

Author

Benoit Cloitre, Jul 27 2002

Extensions

Terms a(9) and beyond from Andrew Howroyd, Apr 20 2021

Status

approved