A337388 - OEIS

A337388

a(n) = Sum_{k=0..n} n^(n-k) * binomial(2*k,k) * binomial(2*n,2*k).

1, 3, 34, 587, 12870, 337877, 10262004, 352436961, 13465074758, 565280386625, 25826066397756, 1274138666796217, 67446164001827356, 3810171540686207283, 228658931521878071080, 14520123059677034441895, 972281769469377542763078, 68443768336740463562683177

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

FORMULA

From Vaclav Kotesovec, Aug 31 2020: (Start)

a(n) ~ (2 + sqrt(n))^(2*n + 1/2) / sqrt(8*Pi*n).

a(n) ~ exp(4*sqrt(n) - 4) * n^(n - 1/4) / sqrt(8*Pi) * (1 + 19/(3*sqrt(n)) + 199/(18*n)). (End)

MATHEMATICA

a[n_] := Sum[If[n == 0, Boole[n == k], n^(n - k)] * Binomial[2*k, k] * Binomial[2*n, 2*k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Aug 25 2020 *)

PROG

(PARI) {a(n) = sum(k=0, n, n^(n-k)*binomial(2*k, k)*binomial(2*n, 2*k))}

CROSSREFS

Main diagonal of A337389.

Cf. A337387.

Sequence in context: A105713 A376137 A367840 * A317653 A143638 A262673

Adjacent sequences: A337385 A337386 A337387 * A337389 A337390 A337391

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 25 2020

STATUS

approved