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 A301499 Total sum of the hook lengths over all partitions of 2n-1 having exactly n parts. 2
 1, 5, 22, 56, 139, 269, 554, 956, 1724, 2830, 4686, 7286, 11539, 17261, 26076, 38130, 55753, 79385, 113350, 158152, 220883, 303346, 415752, 562264, 759601, 1013728, 1350404, 1782342, 2346390, 3064045, 3992698, 5165042, 6666529, 8552739, 10944782, 13932362 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..12000 (terms 1..5000 from Alois P. Heinz) FORMULA a(n) = A180681(2*n-1,n). a(n) ~ exp(Pi*sqrt(2*n/3)) * n / (8*sqrt(3)). - Vaclav Kotesovec, May 27 2018 MAPLE f:= n-> (n-1)*n/2: b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n+f(n)], b(n, i-1)+(p-> p+[0, p[1]*(n+f(i))])(b(n-i, min(n-i, i)))) end: a:= n-> (p-> p[1]*(2*n-1+f(n))+p[2])(b(n-1\$2)): seq(a(n), n=1..45); MATHEMATICA f[n_] := n(n-1)/2; b[n_, i_] := b[n, i] = If[n == 0 || i == 1, {1, n + f[n]}, b[n, i - 1] + Function[p, p + {0, p[[1]] (n + f[i])}][b[n - i, Min[n - i, i]]]]; a[n_] := Function[p, p[[1]] (2n - 1 + f[n]) + p[[2]]][b[n - 1, n - 1]]; Array[a, 45] (* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *) CROSSREFS Cf. A180681. Sequence in context: A272824 A273677 A209116 * A033445 A208946 A245301 Adjacent sequences: A301496 A301497 A301498 * A301500 A301501 A301502 KEYWORD nonn AUTHOR Alois P. Heinz, Mar 22 2018 STATUS approved

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Last modified December 7 23:30 EST 2023. Contains 367662 sequences. (Running on oeis4.)