A391180 a(n) = (2*n-1)! * [x^(2*n-1)] 2*S(x)*(1+S(x)^2)^3 - x*(1+S(x)^2)^2 - S(x), where S(x) satisfies S(x) = Integral (1 + S(x)^2)^2 dx.

0, 28, 1808, 189696, 30500608, 7023401984, 2198253613056, 898678328197120, 465236096336789504, 297558053269111701504, 230454546941593389629440, 212567175789759274485284864, 230267067921944612412497854464, 289477215946040500045195780292608

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..216

Formula

a(n) = A394012(n,1).

a(n) = (2*n-1)! * [x^(2*n-1)] (S(x)'' - 2*x*S(x)' - 2*S(x)) / 2.

Example

S(x) = x + 4*x^3/3! + 88*x^5/5! + 4672*x^7/7! + 454144*x^9/9! + ...
2*S(x)*(1+S(x)^2)^3 - x*(1+S(x)^2)^2 - S(x) = 28*x^3/3! + 1808*x^5/5! + 189696*x^7/7! + 30500608*x^9/9! + ...

Crossrefs

Column k=1 of A394012.

Cf. A281180 ((2*n-1)! * [x^(2*n-1)] S(x)).

Sequence in context: A182400 A333125 A197438 * A263026 A294192 A202811

Adjacent sequences: A391177 A391178 A391179 * A391181 A391182 A391183

Keyword

nonn

Author

Seiichi Manyama, Apr 13 2026

Status

approved