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, 1, 3, 11, 13, 39, 33, 2431, 663, 247, 2717, 80223, 1989, 1062347, 3187041, 16055, 6605027, 77571, 11685817, 1062347, 2002524095, 4405553009, 247, 2717, 497705, 155409680283, 11559397707, 1123416017295, 74894401153, 114727509, 5643476995, 409716429837, 10158258591, 909705199, 233400836858808047, 190964321066297493, 18394643943, 34825896536145, 229850917138557, 17096349208653, 357856262339147, 24291640943843637507, 602272089516784401, 174041631153

Offset

2,3

Comments

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

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

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.

Links

Table of n, a(n) for n=2..45.

Example

The irregular triangle a(n, m) begins:
n\m             1            2            3
2:              1
3:              1
4:              3
5:             11
6:             13           39
7:             33
8:           2431          663
9:            247         2717
10:          8022         1989
11:       1062347      3187041
12:         16055      6605027        77571
13:      11685817      1062347
14:    2002524095   4405553009       249951
15:        497705 155409680283  11559397707
16: 1123416017295  74894401153    114727509
17:    5643476995 409716429837  10158258591
...
row n = 18: 909705199 233400836858808047 190964321066297493 18394643943,
row n = 19: 34825896536145  229850917138557 17096349208653,
row n = 20: 357856262339147 24291640943843637507 602272089516784401 174041631153.
...
For the rationals r(n), n = 2..20, see A274342.

Crossrefs

Cf. A274342.

Sequence in context: A119145 A168454 A181086 * A113049 A370425 A225097

Adjacent sequences: A274340 A274341 A274342 * A274344 A274345 A274346

Keyword

nonn,tabf,frac,easy

Author

Wolfdieter Lang, Jun 20 2016

Status

approved