A247238 a(n) = Stirling2(2*n+1, n).

1, 15, 301, 7770, 246730, 9321312, 408741333, 20415995028, 1144614626805, 71187132291275, 4864251308951100, 362262620784874680, 29206898819153109600, 2534474684137526739000, 235535731151727520125765, 23339590705557273894321960

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..340

Formula

a(n) = A243227(n) / (n-1)!. - Vaclav Kotesovec, Nov 29 2014

a(n) ~ 2^(2*n+1/2) * n^(n+1/2) / (sqrt(Pi) * sqrt(1-c) * exp(n) * c^n * (2-c)^(n+1)), where c = -LambertW(-2*exp(-2)) = 0.4063757399599599... (see A226775). - Vaclav Kotesovec, Nov 29 2014

O.g.f. Sum_{n>=1} n^(2*n+1) * x^n * exp(-n^2*x) / n! = Sum_{n>=1} a(n)*x^n. - Paul D. Hanna, Oct 09 2023

Example

O.g.f.: A(x) = x + 15*x^2 + 301*x^3 + 7770*x^4 + 246730*x^5 + 9321312*x^6 + ... where A(x) = 1^3*x*exp(-1^2*x) + 2^5*exp(-2^2*x)*x^2/2! + 3^7*exp(-3^2*x)*x^3/3! + 4^9*exp(-4^2*x)*x^4/4! + 5^11*exp(-5^2*x)*x^5/5! + ...

Mathematica

Table[StirlingS2[2*n+1, n], {n, 1, 20}] (* Vaclav Kotesovec, Nov 29 2014 *)

Prog

(PARI) vector(50, n, stirling(2*n+1, n, 2)) \\ Colin Barker, Nov 28 2014

Crossrefs

Cf. A048993, A007820, A217899, A243227, A226775.

Sequence in context: A009064 A049381 A051691 * A353145 A135390 A105491

Adjacent sequences: A247235 A247236 A247237 * A247239 A247240 A247241

Keyword

nonn

Author

Vladimir Kruchinin, Nov 28 2014

Status

approved