A352617 -id:A352617 - cp's OEIS frontend

A352326 Expansion of e.g.f.: 1/(2 - exp(x) - sinh(x)).

1, 2, 9, 62, 567, 6482, 88929, 1423382, 26037027, 535813802, 12251630349, 308153112302, 8455276083087, 251333936555522, 8045613346221369, 275950004166050822, 10095559110771678747, 392427366313299119642, 16151459739717643489989

Offset: 0

Seiichi Manyama, Mar 12 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..395

Cf. A000670, A006154, A028296, A094088, A352327, A352617.

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-k)*binomial(n, k)*(1+(k mod 2)), k=1..n))
    end:
seq(a(n), n=0..18); # Alois P. Heinz, Mar 25 2022

m = 18; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - Sinh[x]), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-sinh(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(7) * log((2 + sqrt(7))/3)^(n+1)). - Vaclav Kotesovec, Mar 12 2022

A352624 Expansion of e.g.f. exp(exp(x) + cosh(x) - 2).

Original entry on oeis.org

1, 1, 3, 8, 31, 122, 579, 2886, 16139, 95358, 611111, 4128830, 29709695, 224400022, 1785322699, 14841968646, 129015458195, 1167021383902, 10979895178511, 107113768171950, 1082508179141031, 11308614423992102, 121995294474174963, 1356835055606851286, 15542964081299602811

Offset: 0

Ilya Gutkovskiy, Mar 24 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..566

Cf. A000110, A000807, A001861, A003724, A005046, A352327, A352617.

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-k)*binomial(n-1, k-1)*(2-(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] + Cosh[x] - 2], {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}]

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..floor(n/2)} binomial(n,2*k) * A005046(k) * A000110(n-2*k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k) * A000807(k) * A003724(n-2*k).

cp's OEIS Frontend

A352326 Expansion of e.g.f.: 1/(2 - exp(x) - sinh(x)).

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