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

0,2

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A002416.

Sequence in context: A032469 A006927 A014375 * A145386 A344260 A135327

Adjacent sequences: A135745 A135746 A135747 * A135749 A135750 A135751

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2007

Status

approved