A370293 Decimal expansion of a constant related to the asymptotics of A229452.

4, 9, 0, 1, 5, 2, 8, 1, 2, 2, 2, 8, 9, 7, 8, 7, 3, 0, 4, 7, 7, 8, 0, 1, 2, 8, 8, 9, 1, 6, 1, 0, 4, 9, 5, 5, 5, 3, 6, 6, 1, 6, 4, 0, 2, 1, 4, 0, 1, 2, 7, 3, 1, 0, 5, 2, 5, 1, 4, 8, 9, 7, 8, 3, 7, 1, 9, 9, 3, 2, 5, 2, 4, 2, 1, 6, 8, 9, 9, 3, 9, 7, 2, 2, 7, 8, 0, 4, 4, 2, 6, 7, 3, 1, 4, 0, 1, 6, 3, 9, 2, 9, 8, 3, 5, 4, 9

Offset

-1,1

Comments

In general, for m >= 1, if g.f. = exp(m * Sum_{n>=1} (3*n)!/(3!*n!^3) * x^n/n ), then a(n) ~ m * 2^(2*m-2) * 3^((m-1)/2) * Pi^(m-1) * A370293^m * 3^(3*n) / n^2, cf. A229452 (m=1), A370289 (m=2), A370288 (m=3), A229451 (m=6).

Links

Table of n, a(n) for n=-1..105.

Formula

Equals limit_{n->oo} A229452(n) / (3^(3*n)/n^2).

Equals limit_{n->oo} (A370288(n) * n^2 / (144 * Pi^2 * 3^(3*n)))^(1/3).

Equals limit_{n->oo} (A370289(n) * n^2 / (8 * 3^(1/2) * Pi * 3^(3*n)))^(1/2).

Equals limit_{n->oo} (A229451(n) * n^2 / (2^11 * 3^(7/2) * Pi^5 * 3^(3*n)))^(1/6).

Example

0.0490152812...

Mathematica

RealDigits[E^(HypergeometricPFQ[{1, 1, 4/3, 5/3}, {2, 2, 2}, 1]/27) / (4*Sqrt[3]*Pi), 10, 120][[1]]

Crossrefs

Cf. A229452, A370288, A370289, A229451, A370294, A370295.

Sequence in context: A011348 A198554 A200413 * A021208 A298813 A021675

Adjacent sequences: A370290 A370291 A370292 * A370294 A370295 A370296

Keyword

nonn,cons

Author

Vaclav Kotesovec, Feb 14 2024

Status

approved