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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.
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%I #17 Jan 14 2024 00:14:33

%S 9825688,690587635751,3895157555937180,5870824778815109405,

%T 3785163537257390979782,1331088890498177501120122,

%U 295175742637140311468159615,45387116230097904962420628542,5170069264521752014176860572055,457880645545087313878878724639982

%N 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.

%H Andrew Howroyd, <a href="/A072867/b072867.txt">Table of n, a(n) for n = 1..500</a>

%H J. Lehner, <a href="http://www.jstor.org/stable/2371972">Ramanujan's identities involving the partition function for moduli 11^a</a>, Amer. J. Math., (1943).

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

%o (PARI) a(n) = {numbpart(121*n-5)/121} \\ _Andrew Howroyd_, Apr 20 2021

%Y Cf. A000041.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Jul 27 2002

%E Terms a(9) and beyond from _Andrew Howroyd_, Apr 20 2021