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 1-4 of 4 results.

A296617 Expansion of 1/Sum_{k>=0} (k+1)^(k+1)*x^k.

Original entry on oeis.org

1, -4, -11, -104, -1388, -22980, -446524, -9882944, -244592124, -6684031040, -199824449532, -6488250797312, -227456440349948, -8565880619584896, -345018776767586572, -14805421633750610240, -674514253891722861612, -32522567276377571337728
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2017

Keywords

Crossrefs

Programs

  • PARI
    N=66; x='x+O('x^N); Vec(1/sum(k=0, N, (k+1)^(k+1)*x^k))

A316090 a(n) = [x^n] (Sum_{k=0..n} (k*x)^k)/(Sum_{k=0..n} (-k*x)^k).

Original entry on oeis.org

1, 2, 2, 48, 94, 5694, 12352, 1539850, 3323890, 737028224, 1556371198, 548747031342, 1138137849328, 586694732526026, 1202647898994626, 852409708509446800, 1734703213512100766, 1616070775292699964094, 3273912763003648926368, 3875483980992048140938410
Offset: 0

Views

Author

Seiichi Manyama, Jun 24 2018

Keywords

Crossrefs

Programs

  • PARI
    N=66; x='x+O('x^N); Vec((sum(k=0, N, (k*x)^k))/(sum(k=0, N, (-k*x)^k)))

Formula

a(n) ~ 4 * exp(-1) * n^(n-1) if n is even and a(n) ~ 2 * n^n if n is odd. - Vaclav Kotesovec, Jun 25 2018

A332238 a(n) = n^(n-1) - Sum_{k=1..n-1} k^(k-1) * a(n-k).

Original entry on oeis.org

1, 1, 6, 47, 493, 6446, 101009, 1846631, 38617674, 909844075, 23858239469, 689399172870, 21769608499937, 745964574859679, 27570932237831874, 1093403260892542195, 46315049663202237389, 2087041161850908432022, 99691702658041778953249, 5031814773759672418067623
Offset: 1

Views

Author

Ilya Gutkovskiy, Feb 07 2020

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := a[n] = n^(n - 1) - Sum[k^(k - 1) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 20}]
    nmax = 20; CoefficientList[Series[1 - 1/(1 + Sum[k^(k - 1) x^k, {k, 1, nmax}]), {x, 0, nmax}], x] // Rest

Formula

G.f.: 1 - 1 / (1 + Sum_{k>=1} k^(k-1) * x^k).

A332239 a(n) = n^(n-2) - Sum_{k=1..n-1} k^(k-2) * a(n-k).

Original entry on oeis.org

1, 0, 2, 11, 96, 1058, 14292, 229273, 4268583, 90599501, 2161197285, 57273924968, 1670125069883, 53158796477452, 1834276943996477, 68212851126889959, 2719975462998554200, 115777392670653923870, 5240030485305934701421, 251291379101960875175412
Offset: 1

Views

Author

Ilya Gutkovskiy, Feb 07 2020

Keywords

Crossrefs

Programs

  • Mathematica
    a[n_] := a[n] = n^(n - 2) - Sum[k^(k - 2) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 20}]
    nmax = 20; CoefficientList[Series[1 - 1/(1 + Sum[k^(k - 2) x^k, {k, 1, nmax}]), {x, 0, nmax}], x] // Rest

Formula

G.f.: 1 - 1 / (1 + Sum_{k>=1} k^(k-2) * x^k).
Showing 1-4 of 4 results.