A234324 Central terms of the triangle of central factorial numbers (A008955).

1, 5, 273, 44473, 14739153, 8261931405, 7026231453265, 8439654758970225, 13611213226804376865, 28383081191068916580565, 74326386672885754888959569, 238812235698229573137588936105, 923793013650701305781038113833585, 4235104161629281000608041716747118685

Offset: 0

Author

Reinhard Zumkeller, Dec 24 2013

Keywords

• nonn

Comments

a(n) = A008955(2*n,n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..120

Crossrefs

Cf. A008955, A129505.

Programs

Haskell

a234324 n = a008955 (2 * n) n

Maple

b:= proc(n, k) option remember; `if`(k=0, 1,
      add(b(j-1, k-1)*j^2, j=1..n))
    end:
a:= n-> b(2*n, n):
seq(a(n), n=0..14);  # Alois P. Heinz, Feb 19 2022

Mathematica

Flatten[{1, Table[Coefficient[Expand[Product[1 + k^2*x, {k, 0, 2*n}]], x^n], {n, 1, 15}]}] (* Vaclav Kotesovec, Aug 28 2017 *)
Table[Sum[(-1)^(n-j) * StirlingS1[2*n+1, 2*n+1-j] * StirlingS1[2*n+1, j+1], {j, 0, 2*n}], {n, 0, 15}] (* Vaclav Kotesovec, Aug 28 2017 *)

Formula

a(n) ~ c * d^n * n!^2 / n^(3/2), where d = 30.472614208903344955058219429421999299236787591960717... and c = 0.27436634881777520262458169083560234658... - Vaclav Kotesovec, Aug 28 2017