A331661 E.g.f. A(x) satisfies: d/dx A(x) = 1 + (1/(1 + x)) * A(x/(1 + x)).

1, 1, -3, 6, 30, -720, 9180, -79020, -283500, 41886720, -1580008680, 44344341000, -851982076440, -5914076263200, 1972181136416400, -153108297672649200, 8900721288190544400, -403768420629168268800, 9341444542413659205600, 856476985107522346596000

Offset

1,3

Links

Table of n, a(n) for n=1..20.

Formula

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

Mathematica

terms = 20; A[_] = 0; Do[A[x_] = Normal[Integrate[1 + 1/(1 + x) A[x/(1 + x) + O[x]^(terms + 1)], x] + O[x]^(terms + 1)], terms]; CoefficientList[A[x], x] Range[0, terms]! // Rest
a[1] = 1; a[n_] := a[n] = Sum[(-1)^k Binomial[n - 1, k]^2 k! a[n - k - 1], {k, 0, n - 2}]; Table[a[n], {n, 1, 20}]

Crossrefs

Cf. A307355, A331660.

Sequence in context: A012280 A282132 A002164 * A117805 A154135 A182274

Adjacent sequences: A331658 A331659 A331660 * A331662 A331663 A331664

Keyword

sign

Author

Ilya Gutkovskiy, Jan 23 2020

Status

approved