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A166359 Diagonal sums of the exponential Riordan array [1+x*arctanh(x), x], A166357. 2
1, 3, 15, 197, 6909, 459383, 48252699, 7299708105, 1499523879481, 401147660278507, 135421121289695655, 56285769483090611085, 28237152577765405343285, 16821061018350834178553055 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Aeration of this sequence gives the diagonal sums of A166357.

LINKS

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

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

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 *)

PROG

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

CROSSREFS

Cf. A166356, A166357.

Sequence in context: A060194 A068858 A280772 * A195515 A003505 A270354

Adjacent sequences:  A166356 A166357 A166358 * A166360 A166361 A166362

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 12 2009

STATUS

approved

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Last modified February 17 10:59 EST 2019. Contains 320219 sequences. (Running on oeis4.)