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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. 1

%I #14 Mar 21 2020 09:41:32

%S 1,1,3,11,13,39,33,2431,663,247,2717,80223,1989,1062347,3187041,16055,

%T 6605027,77571,11685817,1062347,2002524095,4405553009,247,2717,497705,

%U 155409680283,11559397707,1123416017295,74894401153,114727509,5643476995,409716429837,10158258591,909705199,233400836858808047,190964321066297493,18394643943,34825896536145,229850917138557,17096349208653,357856262339147,24291640943843637507,602272089516784401,174041631153

%N 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 The length of row n is A008615(n), n >= 2.

%C The numerator triangle is given in A274342 where also details and references are given.

%C 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 The irregular triangle a(n, m) begins:

%e n\m 1 2 3

%e 2: 1

%e 3: 1

%e 4: 3

%e 5: 11

%e 6: 13 39

%e 7: 33

%e 8: 2431 663

%e 9: 247 2717

%e 10: 8022 1989

%e 11: 1062347 3187041

%e 12: 16055 6605027 77571

%e 13: 11685817 1062347

%e 14: 2002524095 4405553009 249951

%e 15: 497705 155409680283 11559397707

%e 16: 1123416017295 74894401153 114727509

%e 17: 5643476995 409716429837 10158258591

%e ...

%e row n = 18: 909705199 233400836858808047 190964321066297493 18394643943,

%e row n = 19: 34825896536145 229850917138557 17096349208653,

%e row n = 20: 357856262339147 24291640943843637507 602272089516784401 174041631153.

%e ...

%e For the rationals r(n), n = 2..20, see A274342.

%Y Cf. A274342.

%K nonn,tabf,frac,easy

%O 2,3

%A _Wolfdieter Lang_, Jun 20 2016

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Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)