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.

A114161 E.g.f.: (3-log(1-2*x))/(1-2*x)^(1/2).

Original entry on oeis.org

3, 5, 17, 91, 667, 6213, 70233, 933819, 14277555, 246772485, 4757596065, 101218975515, 2355535057995, 59520844736325, 1622874515042025, 47490277029572475, 1484579154624005475, 49374909670517201925
Offset: 0

Views

Author

Creighton Dement, Nov 14 2005

Keywords

References

  • C. Dement, Floretion Integer Sequences (work in progress)

Links

Crossrefs

Cf. A114160.

Programs

  • Mathematica
    Range[0, 17]!CoefficientList[ Series[(3 - Log[1 - 2x])/Sqrt[(1 - 2x)], {x, 0, 17}], x] (* or *)
f[n_] := FullSimplify[ 2^n*Gamma[n + 1/2]/Sqrt[Pi]*(3 + PolyGamma[n + 1/2] + EulerGamma + 2Log[2])]; Table[ f[n], {n, 0, 17}] (* Robert G. Wilson v *)
  • PARI
    { my(x = xx + O(xx^30)); Vec(serlaplace((3-log(1-2*x))/(1-2*x)^(1/2))) } \\ Michel Marcus, Jul 06 2015

Formula

a(n) = 2^n*GAMMA(n+1/2)/Pi^(1/2)*(3+Psi(n+1/2) + gamma + 2*log(2)). - Vladeta Jovovic

Extensions

E.g.f. from Vladeta Jovovic
More terms from Robert G. Wilson v, Nov 15 2005

A204234 Permanent of the n-th principal submatrix of A203990.

Original entry on oeis.org

1, 2, 25, 1018, 97617, 18239786, 5881589105, 3009156161810, 2296768410595849, 2494959953768765810, 3716590842220109346457, 7367123790912343973015562, 18955419073428722394855382209, 61999496577719659890376379418138, 253245883804141341597229595842097313
Offset: 0

Views

Author

Clark Kimberling, Jan 13 2012

Keywords

Crossrefs

Cf. A203990.

Programs

  • Maple
    with(LinearAlgebra):
a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> (i+j)*min(i, j)))):
seq(a(n), n=0..16);  # Alois P. Heinz, Nov 14 2016
  • Mathematica
    f[i_, j_] := (i + j) Min[i, j];  (* A203990 *)
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
Table[Det[m[n]], {n, 1, 22}]  (* A114160 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}]  (* A204234 *)

Extensions

a(0)=1 prepended and one more term added by Alois P. Heinz, Nov 14 2016
Showing 1-2 of 2 results.

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

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