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.

A283224 Expansion of exp( Sum_{n>=1} sigma_2(2*n)*x^n/n ) in powers of x.

Original entry on oeis.org

1, 5, 23, 90, 317, 1036, 3192, 9358, 26336, 71542, 188440, 483007, 1208275, 2956941, 7093531, 16709523, 38706389, 88281394, 198474497, 440263342, 964424210, 2087882510, 4470194335, 9471079495, 19868723042, 41291454537, 85049747913, 173697766646
Offset: 0

Views

Author

Seiichi Manyama, Mar 03 2017

Keywords

Links

Crossrefs

Cf. exp( Sum_{n>=1} sigma_k(2*n)*x^n/n ): A182818 (k=1), this sequence (k=2).
Cf. exp( Sum_{n>=1} sigma_2(m*n)*x^n/n ): A000219 (m=1), this sequence (m=2), A283238 (m=3).

Formula

a(n) = (1/n)*Sum_{k=1..n} sigma_2(2*k)*a(n-k). - Seiichi Manyama, Mar 04 2017

A283243 Expansion of exp( Sum_{n>=1} -sigma_2(3*n)*x^n/n ) in powers of x.

Original entry on oeis.org

1, -10, 25, 53, -270, -77, 1057, 610, -2031, -5438, -1953, 17236, 34121, 3351, -103369, -195850, -55471, 468448, 1067785, 764094, -1430780, -4974559, -6242563, 334620, 16946199, 34459888, 29243953, -24503978, -124514921, -205795663, -140256312, 191109263
Offset: 0

Views

Author

Seiichi Manyama, Mar 03 2017

Keywords

Links

Crossrefs

Cf. A283237 (sigma_2(3*n)), A283238 (exp( Sum_{n>=1} sigma_2(3*n)*x^n/n )).
Cf. exp( Sum_{n>=1} -sigma_k(3*n)*x^n/n ): A185654 (k=1), this sequence (k=2).
Cf. exp( Sum_{n>=1} -sigma_2(m*n)*x^n/n ): A073592 (m=1), A283242 (m=2), this sequence (m=3).

Programs

  • PARI
    A283243_vec(m)=Vec(exp(sum(n=1,m,-sigma(3*n,2)*x^n/n)+x*O(x^m))) \\ Yields m+1 terms a(0..m). - M. F. Hasler, Mar 05 2017

Formula

a(n) = -(1/n)*Sum_{k=1..n} sigma_2(3*k)*a(n-k). - Seiichi Manyama, Mar 04 2017

A283244 Expansion of exp( Sum_{n>=1} sigma_3(3*n)*x^n/n ) in powers of x.

Original entry on oeis.org

1, 28, 518, 7439, 90517, 972398, 9472190, 85145743, 715281840, 5668682493, 42691867112, 307312234334, 2124355701646, 14157081285263, 91250293831492, 570441761053192, 3466874635995098, 20526329624103412, 118608374492197651, 669949478060261642
Offset: 0

Views

Author

Seiichi Manyama, Mar 03 2017

Keywords

Links

Crossrefs

Cf. exp( Sum_{n>=1} sigma_k(3*n)*x^n/n ): A182819 (k=1), A283238 (k=2), this sequence (k=3).
Cf. exp( Sum_{n>=1} sigma_3(m*n)*x^n/n ): A023871 (m=1), A282327 (m=2), this sequence (m=3).

Formula

a(n) = (1/n)*Sum_{k=1..n} sigma_3(3*k)*a(n-k). - Seiichi Manyama, Mar 04 2017
Showing 1-3 of 3 results.

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