A166359 Diagonal sums of the exponential Riordan array [1+x*arctanh(x), x], A166357.

1, 3, 15, 197, 6909, 459383, 48252699, 7299708105, 1499523879481, 401147660278507, 135421121289695655, 56285769483090611085, 28237152577765405343285, 16821061018350834178553055

Offset: 0

Author

Paul Barry, Oct 12 2009

Keywords

• easy
• nonn

Comments

Aeration of this sequence gives the diagonal sums of A166357.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A166356, A166357.

Programs

Mathematica

Table[1 + Sum[Binomial[n + k, 2*k] * ((2*k-1)! + (2*k-2)!), {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 17 2018 *)

PARI

a(n)={1 + sum(k=1, n, binomial(n + k, 2*k) * ((2*k-1)! + (2*k-2)!))} \\ Andrew Howroyd, Aug 17 2018

Formula

a(n) = Sum_{k=0..n} C(n+k,2k)*A166356(k).

a(n) ~ sqrt(Pi) * 2^(2*n) * n^(2*n - 1/2) / exp(2*n). - Vaclav Kotesovec, Aug 17 2018