The On-Line Encyclopedia of Integer Sequences (OEIS)

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A165940

G.f.: Sum_{n>=0} a(n)*x^n/2^(n^2+n) = exp( Sum_{n>=1} x^n/[n*2^(n^2)] ).
(history; published version)

#2 by Russ Cox at Fri Mar 30 18:37:18 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Oct 01 2009

Discussion

Fri Mar 30

18:37

OEIS Server: https://oeis.org/edit/global/213

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

G.f.: Sum_{n>=0} a(n)*x^n/2^(n^2+n) = exp( Sum_{n>=1} x^n/[n*2^(n^2)] ).

DATA

1, 2, 10, 152, 7684, 1352096, 852120928, 1960591940480, 16697154282192928, 531801639623740649984, 63854080509077223292639744, 29089348119991257994736112048128

OFFSET

0,2

COMMENTS

Conjectured to consist entirely of integers.

EXAMPLE

G.f.: 1 + 2*x/2^2 + 10*x^2/2^6 + 152*x^3/2^12 + 7684*x^4/2^20 +...

= exp( x/2 + x^2/(2*2^4) + x^3/(3*2^9) + x^4/(4*2^16) +... ).

Evaluated at x=1:

Sum_{n>=0} a(n)/2^(n^2+n) = 1.7021716250154556344906565654972646...

PROG

(PARI) {a(n)=2^(n^2+n)*polcoeff(exp(sum(m=1, n+1, 2^(-m^2)*x^m/m)+x*O(x^n)), n)}

CROSSREFS

Cf. A155200.

KEYWORD

nonn

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), Oct 01 2009

STATUS

approved