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Irregular triangle read by rows: row n gives coefficients when the n-th coefficient of the modular function j (A000521(n)) is written as a linear combination of irreducible characters of the Monster simple group (A001379).
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%I #17 Oct 14 2023 14:04:29

%S 1,1,1,1,1,2,2,1,1,3,3,1,2,1,4,5,3,2,1,1,1

%N Irregular triangle read by rows: row n gives coefficients when the n-th coefficient of the modular function j (A000521(n)) is written as a linear combination of irreducible characters of the Monster simple group (A001379).

%C The coefficients are given as in Thompson's paper. The choice of coefficients is actually ambiguous because of a linear relation with small coefficients between the terms of A001379 (see Wikipedia). - _Andrey Zabolotskiy_, Feb 12 2019

%H J. G. Thompson, <a href="https://doi.org/10.1112/blms/11.3.352">Some numerology between the Fischer-Griess Monster and the elliptic modular function</a>, Bull. London Math. Soc., 11 (1979), 352-353.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Monstrous_moonshine">Monstrous moonshine</a>

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%e Triangle begins:

%e 1,1,

%e 1,1,1,

%e 2,2,1,1,

%e 3,3,1,2,1,

%e 4,5,3,2,1,1,1,

%e ...

%Y Cf. A000521, A001379, A007240, A055791.

%K nonn,tabf,more

%O 1,6

%A _N. J. A. Sloane_, Nov 26 2016