A343707 a(n) = 1 + 2 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).

1, 3, 15, 113, 1145, 14539, 221663, 3943281, 80173345, 1833831619, 46606646175, 1302954958689, 39737420405753, 1312901360002283, 46714233470065999, 1780859204826798401, 72416689888874547969, 3128792006916853876291, 143132514626658326870767, 6911638338982428907738641

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..389

Formula

E.g.f.: exp(x) / (1 + 2 * log(1 - x)).

a(n) = Sum_{k=0..n} binomial(n,k) * A088500(k).

Mathematica

a[n_] := a[n] = 1 + 2 Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[Exp[x]/(1 + 2 Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/(1+2*log(1-x)))) \\ Seiichi Manyama, Oct 20 2021

Crossrefs

Cf. A088500, A201339, A291979, A343709, A343710.

Sequence in context: A300109 A056053 A295758 * A059849 A123853 A357794

Adjacent sequences: A343704 A343705 A343706 * A343708 A343709 A343710

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 26 2021

Status

approved