A331660 E.g.f. A(x) satisfies: d/dx A(x) = 1 + (1/(1 - x)) * A(x/(1 - x)).
1, 1, 5, 32, 280, 3280, 49480, 927560, 21037640, 566134160, 17803754560, 646052181520, 26757321804880, 1252934215973600, 65791336312915520, 3846554938702140320, 248841434876849499040, 17713758333248102781760, 1380631354206969100115200
Offset: 1
Keywords
Programs
-
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[Binomial[n - 1, k]^2 k! a[n - k - 1], {k, 0, n - 2}]; Table[a[n], {n, 1, 20}]
Formula
a(1) = 1; a(n+1) = Sum_{k=0..n-1} binomial(n,k)^2 * k! * a(n-k).