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 1-2 of 2 results.

A353925 Product_{n>=1} (1 + a(n)*x^n) = 1 + Sum_{n>=1} phi(n)*x^n, where phi = A000010.

Original entry on oeis.org

1, 1, 1, 1, 2, -2, 4, -3, 4, -6, 14, -18, 30, -32, 48, -73, 128, -182, 286, -394, 578, -804, 1386, -1936, 3172, -4298, 7102, -10202, 16414, -23798, 38056, -54997, 86658, -125180, 203396, -292650, 475536, -685314, 1100728, -1619952, 2601166, -3808952, 6114666, -9045400, 14352568
Offset: 1

Views

Author

Ilya Gutkovskiy, May 11 2022

Keywords

Crossrefs

Cf. A000010, A320778, A328774, A353923, A353924, A353926.

Programs

  • Mathematica
    A[m_, n_] := A[m, n] = Which[m == 1, EulerPhi[n], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 45]

A353948 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} phi(n)*x^n, where phi = A000010.

Original entry on oeis.org

1, 0, 1, 0, 2, -3, 4, -4, 4, -10, 14, -25, 30, -48, 48, -86, 128, -192, 286, -470, 578, -1000, 1386, -2423, 3172, -5198, 7102, -11994, 16414, -25820, 38056, -61444, 86658, -141564, 203396, -324640, 475536, -767110, 1100728, -1810752, 2601166, -4118166, 6114666
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2022

Keywords

Crossrefs

Cf. A000010, A320778, A328774, A353925, A353945, A353947, A353949.

Programs

  • Mathematica
    A[m_, n_] := A[m, n] = Which[m == 1, EulerPhi[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, 43]
Showing 1-2 of 2 results.

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