A135748 a(n) = Sum_{k=0..n} binomial(n,k)*2^(k^2).

1, 3, 21, 567, 67689, 33887403, 68921796861, 563431696713567, 18451249599365935569, 2418017680197896730749523, 1267674779574792745831097365221, 2658469935859419140387217204140789127, 22300777100086187451068223319189800258419769

Offset: 0

Author

Paul D. Hanna, Nov 27 2007

Keywords

• nonn

Comments

a(n) is the number of directed graphs on any subset of a set of n labeled nodes, allowing self-loops (cf. A002416). - Brent A. Yorgey, Mar 23 2021

Links

• G. C. Greubel, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A002416.

Programs

Mathematica

Table[Sum[Binomial[n,k]2^k^2,{k,0,n}],{n,0,15}] (* Harvey P. Dale, May 30 2013 *)

PARI

{a(n)=sum(k=0,n,binomial(n,k)*2^(k^2))}

Formula

a(n) ~ 2^(n^2). - Vaclav Kotesovec, Nov 27 2017