A352326 -id:A352326 - cp's OEIS frontend

A352327 Expansion of e.g.f.: 1/(3 - exp(x) - cosh(x)).

1, 1, 4, 19, 130, 1081, 10894, 127639, 1711210, 25798141, 432212134, 7964801659, 160121522290, 3487254825601, 81790592435374, 2055350489070079, 55093108433421370, 1569052795651631461, 47315282424232826614, 1506074331671551028899

Offset: 0

Seiichi Manyama, Mar 12 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..414

Cf. A000670, A006154, A094088, A352326, A352624.

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-k)*binomial(n, k)*(2-(k mod 2)), k=1..n))
    end:
seq(a(n), n=0..19); # Alois P. Heinz, Mar 25 2022

m = 19; Range[0, m]! * CoefficientList[Series[1/(3 - Exp[x] - Cosh[x]), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(3-exp(x)-cosh(x))))

a(n) = if(n==0, 1, sum(k=1, n, (3+(-1)^k)/2*binomial(n, k)*a(n-k)));

a(0) = 1; a(n) = Sum_{k=1..n} (3+(-1)^k)/2 * binomial(n,k) * a(n-k).

a(n) ~ n! / (sqrt(6) * log(1 + sqrt(2/3))^(n+1)). - Vaclav Kotesovec, Mar 12 2022

A352617 Expansion of e.g.f. exp( exp(x) + sinh(x) - 1 ).

Original entry on oeis.org

1, 2, 5, 16, 60, 254, 1199, 6206, 34827, 210264, 1355992, 9288954, 67279309, 513149498, 4107383185, 34398823888, 300629113292, 2735356900806, 25857446103571, 253472859754918, 2572266378189583, 26981781750668760, 292136508070103208, 3260640536587635410, 37472102225288489529

Offset: 0

Ilya Gutkovskiy, Mar 24 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..565

Cf. A000110, A001861, A003724, A005046, A352279, A352326.

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-k)*binomial(n-1, k-1)*(1+(k mod 2)), k=1..n))
    end:
seq(a(n), n=0..24);  # Alois P. Heinz, Mar 24 2022

nmax = 24; CoefficientList[Series[Exp[Exp[x] + Sinh[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = (1/2) Sum[Binomial[n - 1, k - 1] (3 - (-1)^k) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]

my(x='x+O('x^30)); Vec(serlaplace(exp( exp(x) + sinh(x) - 1 ))) \\ Michel Marcus, Mar 24 2022

a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} binomial(n-1,k-1) * (3 - (-1)^k) * a(n-k).
a(n) = Sum_{k=0..n} binomial(n,k) * A000110(k) * A003724(n-k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k) * A005046(k) * A352279(n-2*k).

cp's OEIS Frontend

A352327 Expansion of e.g.f.: 1/(3 - exp(x) - cosh(x)).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

PARI

Formula

A352617 Expansion of e.g.f. exp( exp(x) + sinh(x) - 1 ).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula