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.

A353605 Product_{n>=1} (1 + a(n)*x^n) = 1 + Sum_{n>=1} prime(n+1)*x^n.

Original entry on oeis.org

3, 5, -8, 35, -52, 118, -320, 1597, -2016, 6616, -16064, 40516, -122552, 381606, -903176, 4389807, -7597004, 22835416, -61172890, 188526110, -486889660, 1550995910, -4093173788, 11608277912, -33815484714, 105179650108, -279683446078, 883705997682, -2366564864546
Offset: 1

Views

Author

Ilya Gutkovskiy, May 07 2022

Keywords

Crossrefs

Cf. A006005, A065091, A147557, A353606.

Programs

  • Mathematica
    nn = 29; f[x_] := Product[(1 + a[n] x^n), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - Sum[Prime[k + 1] x^k, {k, 1, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten

A353950 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} prime(n+1)*x^n.

Original entry on oeis.org

3, -4, -8, -26, -52, -126, -320, -1214, -2016, -7068, -16064, -48142, -122552, -390574, -903176, -3549556, -7597004, -22902332, -61172890, -198872948, -486889660, -1555059566, -4093173788, -12448334478, -33815484714, -105268420776, -279683446078, -894795490384, -2366564864546
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2022

Keywords

Crossrefs

Cf. A006005, A065091, A147557, A305882, A353605, A353606, A353951.

Programs

  • Mathematica
    A[m_, n_] := A[m, n] = Which[m == 1, Prime[n + 1], 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, 29]

A353951 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + x + Sum_{n>=2} prime(n-1)*x^n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, -1, -2, -3, -2, 4, -1, 5, 2, -4, -8, -9, -3, -3, 12, 19, -6, 6, -38, -27, -32, 13, 56, 50, 99, -49, -135, -162, -258, 83, 114, 468, 359, -40, -390, -1215, -791, -526, 876, 2640, 1816, 1673, -3404, -4516, -6527, -3640, 5320, 9282, 18019, 7210
Offset: 1

Views

Author

Ilya Gutkovskiy, May 12 2022

Keywords

Crossrefs

Cf. A008578, A147557, A305882, A353605, A353606, A353950.

Programs

  • Mathematica
    A[m_, n_] := A[m, n] = Which[m == 1, If[n == 1, 1, Prime[n - 1]], 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, 55]
Showing 1-3 of 3 results.

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

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