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A274343 Irregular triangle read by rows giving the denominators of the coefficients of the Eisenstein series G_{2*n} multiplied by 2*n-1, for n >= 2. Also Laurent coefficients of Weierstrass's P function.

%I A274343 #14 Mar 21 2020 09:41:32
%S A274343 1,1,3,11,13,39,33,2431,663,247,2717,80223,1989,1062347,3187041,16055,
%T A274343 6605027,77571,11685817,1062347,2002524095,4405553009,247,2717,497705,
%U A274343 155409680283,11559397707,1123416017295,74894401153,114727509,5643476995,409716429837,10158258591,909705199,233400836858808047,190964321066297493,18394643943,34825896536145,229850917138557,17096349208653,357856262339147,24291640943843637507,602272089516784401,174041631153
%N A274343 Irregular triangle read by rows giving the denominators of the coefficients of the Eisenstein series G_{2*n} multiplied by 2*n-1, for n >= 2. Also Laurent coefficients of Weierstrass's P function.
%C A274343 The length of row n is A008615(n), n >= 2.
%C A274343 The numerator triangle is given in A274342 where also details and references are given.
%C A274343 a(n) = denominator(r(n)) where the rationals r(n) are reduced to lowest terms obtained from the c(n) recurrence given in a comment of A274342 as coefficients of powers of c2 and c3 corresponding to the partitions of n with parts 2 and 3 only, when sorted with increasing number of parts.
%e A274343 The irregular triangle a(n, m) begins:
%e A274343 n\m             1            2            3
%e A274343 2:              1
%e A274343 3:              1
%e A274343 4:              3
%e A274343 5:             11
%e A274343 6:             13           39
%e A274343 7:             33
%e A274343 8:           2431          663
%e A274343 9:            247         2717
%e A274343 10:          8022         1989
%e A274343 11:       1062347      3187041
%e A274343 12:         16055      6605027        77571
%e A274343 13:      11685817      1062347
%e A274343 14:    2002524095   4405553009       249951
%e A274343 15:        497705 155409680283  11559397707
%e A274343 16: 1123416017295  74894401153    114727509
%e A274343 17:    5643476995 409716429837  10158258591
%e A274343 ...
%e A274343 row n = 18: 909705199 233400836858808047 190964321066297493 18394643943,
%e A274343 row n = 19: 34825896536145  229850917138557 17096349208653,
%e A274343 row n = 20: 357856262339147 24291640943843637507 602272089516784401 174041631153.
%e A274343 ...
%e A274343 For the rationals r(n), n = 2..20, see A274342.
%Y A274343 Cf. A274342.
%K A274343 nonn,tabf,frac,easy
%O A274343 2,3
%A A274343 _Wolfdieter Lang_, Jun 20 2016