A098696 Main diagonal of array in A073146.

1, 4, 104, 6544, 765344, 143639104, 39511297664, 14979797833984, 7487442077817344, 4770988535512474624, 3774873839360539879424, 3630982576832133263233024, 4172729918808369709126098944

Offset: 0

Author

Ralf Stephan, Sep 23 2004

Keywords

• nonn

Comments

Diagonal of Euler-Seidel matrix with start sequence A000670.

Crossrefs

Cf. A000670, A073146.

Programs

Mathematica

Table[Sum[Binomial[n, k] * Sum[StirlingS2[2*n-k, j]*j!, {j, 0, 2*n-k}],{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, May 03 2015 *)

Formula

a(n) = Sum_{k=0..n} binomial(n, k) * A000670(2*n-k).

a(n) ~ (2*n)! / (sqrt(2) * (log(2))^(2*n+1)). - Vaclav Kotesovec, May 03 2015

a(n) = Sum_{k>=0} (k*(k + 1))^n/2^(k+1). - Ilya Gutkovskiy, Jun 29 2019

Extensions

Offset corrected by Vaclav Kotesovec, May 03 2015