A104098 a(n) = Sum_{k=1..n} binomial(n-1, k-1)*A008292(n, k) for n >= 1.

1, 2, 10, 68, 606, 6612, 85492, 1277096, 21641590, 410144180, 8595133548, 197346180792, 4926442358124, 132847425483528, 3848398710032616, 119187270233781456, 3929892162743796390, 137444081992905303540, 5082053733073190713660, 198081684441819323760920

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..201

Formula

a(n) ~ sqrt(3) * 2^(n-1) * n^n / exp(n). - Vaclav Kotesovec, Oct 09 2020, modified for offset 1, Oct 29 2023

Example

   1 = 1*1
   2 = 1*1 +  1*1
  10 = 1*1 +  2*4 + 1*1
  68 = 1*1 + 3*11 + 3*11 + 1*1
  ...

Maple

a := n -> local k; add(binomial(n - 1, k - 1) * combinat:-eulerian1(n, k - 1), k = 1..n): seq(a(n), n = 1..20);  # Peter Luschny, Oct 29 2023

Mathematica

Table[Sum[Binomial[n-1, k-1] * Sum[(-1)^j * (k-j)^n * Binomial[n+1, j], {j, 0, k}], {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 09 2020 *)

Crossrefs

Cf. A008292, A011818.

Sequence in context: A136658 A329475 A165968 * A056755 A123617 A325054

Adjacent sequences: A104095 A104096 A104097 * A104099 A104100 A104101

Keyword

nonn

Author

Paul D. Hanna, Mar 29 2006

Extensions

Offset changed by Georg Fischer, Oct 29 2023

Status

approved