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.

A353945 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} tau(n)*x^n, where tau = A000005.

Original entry on oeis.org

1, 1, 0, 0, -1, 1, -1, 0, 1, -2, 0, 1, -1, -2, 2, 1, -2, -2, 2, 0, -4, 0, 3, -3, 3, -3, -2, -1, 1, 8, -15, 0, 17, -14, -1, -3, 9, -5, -18, 23, -10, -18, 24, -17, -17, 18, 27, -48, -37, 72, 45, -119, -11, 148, -98, -28, 65, -57, 24, -95, 213, -363, -173, 704, -435
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2022

Keywords

Crossrefs

Cf. A000005, A320779, A328775, A353923, A353947, A353948, A353949.

Programs

  • Mathematica
    A[m_, n_] := A[m, n] = Which[m == 1, DivisorSigma[0, n], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 65]

Formula

Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} x^n / (1 - x^n).

A353947 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} sigma(n)*x^n, where sigma = A000203.

Original entry on oeis.org

1, 2, 1, -1, -3, -1, -1, -3, 3, -17, -1, -6, 3, -22, 1, -28, 1, -68, 7, -262, -13, -199, 27, -341, 29, -647, 3, -1431, -25, -476, -81, -4816, 89, -7384, 637, -17565, -275, -27043, -263, -107113, -453, -98469, -583, -208302, 8121, -371798, -6661, -743344, 3045, -1060666
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2022

Keywords

Crossrefs

Cf. A000203, A320780, A328776, A353924, A353945, A353948, A353949.

Programs

  • Mathematica
    A[m_, n_] := A[m, n] = Which[m == 1, DivisorSigma[1, n], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 50]

Formula

Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} x^n / (1 - x^n)^2.

A353949 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} mu(n)*x^n, where mu = A008683.

Original entry on oeis.org

1, -2, 0, -3, -1, 4, -4, -4, -7, 14, -10, -2, -5, 6, 19, -102, 70, -95, 138, -314, 174, 48, -70, -156, -797, 2028, -2048, 1989, -3479, 4277, -2080, -11462, 7923, -12448, 32218, -68038, 68683, -64844, 82847, -170573, -24942, 257846, -422887, 599115, -1225608, 2072993
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2022

Keywords

Crossrefs

Cf. A008683, A320781, A353926, A353927, A353945, A353947, A353948.

Programs

  • Mathematica
    A[m_, n_] := A[m, n] = Which[m == 1, MoebiusMu[n], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 46]
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.