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 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. 3
 1, 5, 161, 14575, 2671669, 833607138, 397984073059, 270609861663900, 248922595132336125, 298037055910658382175, 450755158919281716609746, 840770855566250627155136090, 1896671776639253430025972662743, 5091278095597325836977485757711800, 16040729445423172146341201903726496024, 58625927208516621021861960954787323034320, 246047331971247756894582227572712664877434765, 1175344062721738572130662103242054758238706829325 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 19 03:54 EST 2020. Contains 331031 sequences. (Running on oeis4.)