A274712 a(n) = A008277(3*n-1,n) / (n*(n+1)/2) for n>=1, where A008277 are the Stirling numbers of the second kind.

1, 5, 161, 14575, 2671669, 833607138, 397984073059, 270609861663900, 248922595132336125, 298037055910658382175, 450755158919281716609746, 840770855566250627155136090, 1896671776639253430025972662743, 5091278095597325836977485757711800, 16040729445423172146341201903726496024, 58625927208516621021861960954787323034320, 246047331971247756894582227572712664877434765, 1175344062721738572130662103242054758238706829325

Offset

1,2

Links

Paul D. Hanna, Table of n, a(n) for n = 1..100

Formula

a(n) = A274713(n) / (n*(n+1)/2), where A274713(n) is the number of partitions of a {3*n-1}-set into n nonempty subsets.

a(n) = 1/n! * Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * k^(3*n-1) / (n*(n+1)/2).

a(n) ~ sqrt(2) * 3^(3*n-1) * n^(2*n-7/2) / (exp(2*n) * c^n * (3-c)^(2*n-1) * sqrt(Pi*(1-c))), where c = -LambertW(-3*exp(-3)) = 0.1785606278779211... = -A226750. - Vaclav Kotesovec, Jul 06 2016

Prog

(PARI) {a(n) = polcoeff( 1/prod(k=1, n, 1-k*x +x*O(x^(2*n))), 2*n-1) / (n*(n+1)/2)}
for(n=1, 20, print1(a(n), ", "))
(PARI) {a(n) = abs( stirling(3*n-1, n, 2) / (n*(n+1)/2) )}
for(n=1, 20, print1(a(n), ", "))
(PARI) {a(n) = 1/n! * sum(k=0, n, (-1)^(n-k) * binomial(n, k) * k^(3*n-1)) / (n*(n+1)/2)}
for(n=1, 20, print1(a(n), ", "))

Crossrefs

Cf. A274713.

Sequence in context: A136368 A229163 A322747 * A117068 A185832 A301667

Adjacent sequences: A274709 A274710 A274711 * A274713 A274714 A274715

Keyword

nonn

Author

Paul D. Hanna, Jul 03 2016

Status

approved