[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A331661
E.g.f. A(x) satisfies: d/dx A(x) = 1 + (1/(1 + x)) * A(x/(1 + x)).
1
1, 1, -3, 6, 30, -720, 9180, -79020, -283500, 41886720, -1580008680, 44344341000, -851982076440, -5914076263200, 1972181136416400, -153108297672649200, 8900721288190544400, -403768420629168268800, 9341444542413659205600, 856476985107522346596000
OFFSET
1,3
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
Sequence in context: A012280 A282132 A002164 * A117805 A154135 A182274
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jan 23 2020
STATUS
approved