A351881 -id:A351881 - cp's OEIS frontend

A351880 Expansion of e.g.f. 1 / (1 - x)^cos(x).

1, 1, 2, 3, 6, 15, 105, 924, 8204, 73461, 700005, 7323976, 84472146, 1064285027, 14492861747, 211738655608, 3302847261448, 54800458320345, 963864555797385, 17914985159719376, 350861004976886190, 7221748369472388727, 155853930324297011719, 3519121773604369318856

Offset: 0

Ilya Gutkovskiy, Feb 23 2022

nonn

Cf. A007118, A007119, A009192, A009410, A298374, A351881.

nmax = 23; CoefficientList[Series[1/(1 - x)^Cos[x], {x, 0, nmax}], x] Range[0, nmax]!

my(x='x+O('x^30)); Vec(serlaplace(1/(1-x)^cos(x))) \\ Michel Marcus, Feb 23 2022

a(0) = 1; a(n) = -Sum_{k=1..n} (-1)^k * binomial(n-1,k-1) * A009410(k) * a(n-k).

a(n) ~ n! * n^(cos(1)-1) / Gamma(cos(1)). - Vaclav Kotesovec, Feb 23 2022

A351883 Expansion of e.g.f. 1 / (1 - x)^sech(x).

Original entry on oeis.org

1, 1, 2, 3, 6, 35, 285, 2044, 13804, 108093, 1083405, 12281896, 143452386, 1763156031, 23845410407, 353626471808, 5579871336488, 92609430408361, 1627509065584185, 30379312334903408, 598533509334403470, 12366674489588950555, 267527916985316556019

Offset: 0

Ilya Gutkovskiy, Feb 23 2022

nonn

Cf. A009197, A009435, A351881, A351882.

nmax = 22; CoefficientList[Series[1/(1 - x)^Sech[x], {x, 0, nmax}], x] Range[0, nmax]!

my(x='x+O('x^30)); Vec(serlaplace(1/(1-x)^(1/cosh(x)))) \\ Michel Marcus, Feb 23 2022

a(0) = 1; a(n) = -Sum_{k=1..n} (-1)^k * binomial(n-1,k-1) * A009435(k) * a(n-k).

a(n) ~ n! / (Gamma(1/cosh(1)) * n^(1 - 1/cosh(1))). - Vaclav Kotesovec, Feb 24 2022

cp's OEIS Frontend

A351880 Expansion of e.g.f. 1 / (1 - x)^cos(x).

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