cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A283164 Expansion of exp( Sum_{n>=1} -sigma(6*n)*x^n/n ) in powers of x.

Original entry on oeis.org

1, -12, 58, -133, 95, 194, -418, 97, 325, -99, -238, 169, -217, 131, 190, -145, 441, -647, 169, -527, 72, 1129, 313, -972, 2, -491, -565, 1944, -1175, -216, 972, 863, -1259, 288, 0, -1155, -1355, -207, 2925, 1753, 1402, -2387, -2257, -1030, 315, 432, -72, 1621, 358
Offset: 0

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Author

Seiichi Manyama, Mar 02 2017

Keywords

Links

Crossrefs

Cf. A224613 (sigma(6*n)), A283119 (exp( Sum_{n>=1} sigma(6*n)*x^n/n )).
Cf. exp( Sum_{n>=1} -sigma(k*n)*x^n/n ): A115110 (k=2), A185654 (k=3), A283163 (k=4), A282937 (k=5), this sequence (k=6), A282942 (k=7), A283168 (k=8), A283169 (k=9).

Formula

G.f.: Product_{n>=1} (1 - x^n)^12 * (1 - x^(6*n))/((1 - x^(2*n))^4 * (1 - x^(3*n))^3).
a(n) = -(1/n)*Sum_{k=1..n} sigma(6*k)*a(n-k). - Seiichi Manyama, Mar 04 2017

A283168 Expansion of exp( Sum_{n>=1} -sigma(8*n)*x^n/n ) in powers of x.

Original entry on oeis.org

1, -15, 97, -350, 770, -1133, 1540, -2731, 4230, -3960, 3402, -6580, 9167, -5390, 4310, -11061, 12320, -5306, 2030, -7530, 14784, -4340, -10119, -9240, 20090, 11438, -17275, -4928, 2270, 14080, -26840, 7700, 16646, 24640, -53760, 7449, 10780, 46200, -61600
Offset: 0

Views

Author

Seiichi Manyama, Mar 02 2017

Keywords

Links

Crossrefs

Cf. A283120 (exp( Sum_{n>=1} sigma(8*n)*x^n/n )), A283122 (sigma(8*n)).
Cf. exp( Sum_{n>=1} -sigma(k*n)*x^n/n ): A115110 (k=2), A185654 (k=3), A283163 (k=4), A282937 (k=5), A283164 (k=6), A282942 (k=7), this sequence (k=8), A283169 (k=9).

Formula

G.f.: Product_{n>=1} (1 - x^n)^15/(1 - x^(2*n))^7.
a(n) = -(1/n)*Sum_{k=1..n} sigma(8*k)*a(n-k). - Seiichi Manyama, Mar 04 2017

A283169 Expansion of exp( Sum_{n>=1} -sigma(9*n)*x^n/n ) in powers of x.

Original entry on oeis.org

1, -13, 65, -126, -117, 988, -1377, -1157, 5382, -4419, -4212, 12519, -11179, -5058, 27378, -23005, -16488, 44343, -30249, -18513, 73710, -56259, -38741, 93483, -69570, -23778, 137266, -90396, -74079, 140292, -108621, -39249, 222624, -145710, -99234
Offset: 0

Views

Author

Seiichi Manyama, Mar 02 2017

Keywords

Links

Crossrefs

Cf. A283121 (exp( Sum_{n>=1} sigma(9*n)*x^n/n )), A283123 (sigma(9*n)).
Cf. exp( Sum_{n>=1} -sigma(k*n)*x^n/n ): A115110 (k=2), A185654 (k=3), A283163 (k=4), A282937 (k=5), A283164 (k=6), A282942 (k=7), A283168 (k=8), this sequence (k=9).

Formula

G.f.: Product_{n>=1} (1 - x^n)^13/(1 - x^(3*n))^4.
a(n) = -(1/n)*Sum_{k=1..n} sigma(9*k)*a(n-k). - Seiichi Manyama, Mar 04 2017
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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