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.

A384335 Expansion of g.f.: cosh(7*arctanh(6*sqrt(x))).

Original entry on oeis.org

1, 882, 150822, 14431284, 1052738694, 65805858972, 3724625506140, 196735568051880, 9876433300259526, 476865669055691916, 22326189769485093492, 1019514155600973935448, 45604820017276687744668, 2004918589790139365901720, 86848896758228990302070520, 3714470212008822424691576400
Offset: 0

Views

Author

Karol A. Penson, May 26 2025

Keywords

Crossrefs

Cf. A383928.

Programs

  • Mathematica
    CoefficientList[Series[Cosh[7*ArcTanh[6*Sqrt[x]]],{x,0,15}],x] (* Stefano Spezia, May 26 2025 *)

Formula

a(n) = 9^n*(512*n^3 + 64*n^2 + 144*n + 15)*(2*n)!/(15*(n!)^2).
G.f.: (1 + 756*x + 45360*x^2 + 326592*x^3)/(-36*x + 1)^(7/2).
E.g.f.: (1/5)*exp(18*x)*((5 + 4320*x + 290304*x^2 + 3981312*x^3)*BesselI(0,18*x)+((864*x + 179712*x^2 + 3981312*x^3)*BesselI(1,18*x))).

A384417 Expansion of g.f. cosh(9*arctanh(8*sqrt(x))).

Original entry on oeis.org

1, 2592, 1230336, 294469632, 49690312704, 6822215811072, 818458027622400, 89312567167549440, 9086229152658358272, 875874088323041460224, 80899222450192930308096, 7217466034064795168145408, 625687045828728598806134784, 52946875811413468120885493760, 4389120887020725640048536453120
Offset: 0

Views

Author

Karol A. Penson, May 28 2025

Keywords

Crossrefs

Cf. A383928, A384335, A285043, A285044, A285045, A285046.

Programs

  • Maple
    seq(coeff(series((1 + 2304*x + 516096*x^2 + 22020096*x^3 + 150994944*x^4)/(-64*x + 1)^(9/2), x, 15), x, k), k=0..14);
  • Mathematica
    CoefficientList[Series[Cosh[9*ArcTanh[8*Sqrt[x]]],{x,0,14}],x] (* Stefano Spezia, May 29 2025 *)

Formula

a(n) = 16^n*(105 + 400*n + 3392*n^2 + 512*n^3 + 4096*n^4)*(2*n)!/(105*(n!)^2).
O.g.f.: (1 + 2304*x + 516096*x^2 + 22020096*x^3 + 150994944*x^4)/(-64*x + 1)^(9/2).
E.g.f.: exp(32*x)*((105 + 512*x*(269 + 256*x*(73 + 512*x)))*BesselI(0, 32*x) + 512*x*(25 + 256*x*(65 + 512*x))*BesselI(1, 32*x))/105 + (131072*x*hypergeom([3/2, 2, 2], [1, 1, 1], 64*x))/105.

A384542 Expansion of g.f. sinh(7*arctanh(14*sqrt(x)))/(98*sqrt(x)).

Original entry on oeis.org

1, 1666, 1090054, 485318932, 176760328262, 56963958713340, 16909346921973660, 4732136004374122344, 1266899066122354262598, 327667319343098397330668, 82435716917761454374571444, 20275150472587631020453400984, 4893425028040341625551135687452, 1162305136998381407493307772297560
Offset: 0

Views

Author

Karol A. Penson, Jun 02 2025

Keywords

Crossrefs

Cf. A383928, A384335, A285043, A285044, A285045, A285046, A384417.

Programs

  • Mathematica
    a[n_]:=49^n*(105 + 464*n + 704*n^2 + 512*n^3)*(2*n)!/(105*(n!)^2); Array[a,14,0] (* Stefano Spezia, Jun 02 2025 *)

Formula

a(n) = 49^n*(105 + 464*n + 704*n^2 + 512*n^3)*(2*n)!/(105*(n!)^2).
O.g.f.: (1 + 980*x + 115248*x^2 + 1075648*x^3)/(-196*x + 1)^(7/2).
E.g.f.: exp(98*x)*(BesselI(0, 98*x)*(275365888*x^3 + 5444096*x^2 + 23520*x + 15) + 224*x*BesselI(1, 98*x)*(1229312*x^2 + 18032*x + 29))/15.
Showing 1-3 of 3 results.

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