The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A132039

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Showing entries 1-10 | older changes

A132039

E.g.f.: A(x) = Sum_{n>=0} a(n)*x^n/n! = exp( Sum_{n>=0} a(n)*x^(n+1)/(n+1) ) with a(0) = 1.
(history; published version)

#13 by N. J. A. Sloane at Thu Aug 04 22:34:18 EDT 2016

STATUS

proposed

approved

#12 by Johannes W. Meijer at Wed Aug 03 13:33:59 EDT 2016

STATUS

editing

proposed

#11 by Johannes W. Meijer at Wed Aug 03 13:33:18 EDT 2016

MAPLE

A132039 := proc(n) option remember: if n=0 then 1 else add((n-1)!/k!*A132039(k)*A132039(n-1-k), k=0..n-1) fi: end: seq(A132039(n), n=0..13);

STATUS

proposed

editing

#10 by Johannes W. Meijer at Wed Aug 03 13:28:32 EDT 2016

STATUS

editing

proposed

#9 by Johannes W. Meijer at Wed Aug 03 13:28:16 EDT 2016

COMMENTS

Shifts A132039(n-1), n >= 1, one place left under MNL transform, see A274760. Pointed out by Paul D. Hanna. - Johannes W. Meijer, Aug 03 2016

MAPLE

nmax:=13: t1 := add(a(n)*x^n/n!, n=0..nmax): t2 := series(exp(add(a(n)*x^(n+1)/(n+1), n=0..nmax)), x, nmax+1): a(0) := 1: for n from 1 to nmax do a(n) := n!*coeff(t2, x, n) od: A132039 := proc(n): a(n) end: seq(A132039(n), n=0..nmax); # Johannes W. Meijer, Aug 03 2016

CROSSREFS

Cf. A274760, A007548, A275593, A275594.

KEYWORD

nonn,eigen

STATUS

approved

editing

#8 by Charles R Greathouse IV at Fri May 10 12:45:50 EDT 2013

FORMULA

a(n+1) = Sum_{k=0..n} n!/k!*a(k)*a(n-k). - _Vladeta Jovovic (vladeta(AT)eunet.rs), _, Jul 08 2008

Discussion

Fri May 10

12:45

OEIS Server: https://oeis.org/edit/global/1911

#7 by Paul D. Hanna at Wed Jun 13 09:17:03 EDT 2012

STATUS

editing

approved

#6 by Paul D. Hanna at Wed Jun 13 09:16:49 EDT 2012

DATA

1, 1, 2, 8, 74, 2122, 267292, 194323504, 980945301116, 39560543100700028, 14356125485861852659544, 52095666080476161483596777824, 2079492908949143825845786572097662328, 996080457608702027557335524810508733871848312

EXAMPLE

E.g.f.: A(x) = 1 + 1x 1*x + 2x2*x^2/2! + 8x8*x^3/3! + 74x74*x^4/4! + 2122x2122*x^5/5! +...;

E.g.f.: A(x) = exp(x + 1x1*x^2/2 + 2x2*x^3/3 + 8x8*x^4/4 + 74x74*x^5/5 + 2122x2122*x^6/6 +...) .

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:37:04 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Aug 07 2007

Discussion

Fri Mar 30

18:37

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

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

FORMULA

a(n+1) = Sum_{k=0..n} n!/k!*a(k)*a(n-k). - Vladeta Jovovic (vladeta(AT)Euneteunet.yurs), Jul 08 2008

KEYWORD

nonn,new

nonn