0,3

Conjecture: this sequence is the inverse binomial transform of A075272 or, equivalently, the inverse binomial transform of the BinomialMean transform of A075271. - John W. Layman (layman(AT)math.vt.edu), Sep 12 2002

To win a game, you must flip n+1 heads in a row, where n is the total number of tails flipped so far. Then the probability of winning for the first time after n tails is A005329 / A006125 . The probability of having won before n+1 tails is A114604 / A006125 . - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Dec 14 2005

Number of upper triangular n X n (0,1)-matrices with no zero rows. - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 10 2008

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 17 2009: (Start)

Equals the q-Fibonacci series for q = (-2), and the series prefaced with a 1:

(1, 1, 1, 3, 21,...) dot (1, -2, 4, -8,...) if n is even, and (-1, 2, -4, 8,...) if n is odd.

Examples: a(3) = 21 = (1, 1, 1, 3) dot (-1, 2, -4, 8) = (-1, 2, -4, 24).

a(4) = 315 = (1, 1, 1, 3, 21) dot (1, -2, 4, -8 16) = (1, -2, 4, -24, 336). (End)

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Andresen, E.; Kjeldsen, K.; On certain subgraphs of a complete transitively directed graph. Discrete Math. 14 (1976), no. 2, 103-119.

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

T. D. Noe, Table of n, a(n) for n=0..50

Index entries for sequences related to factorial numbers

Better description from Leslie Ann Goldberg (leslie(AT)dcs.warwick.ac.uk).

a(n)/2^(n*(n+1)/2) -> c = 0.2887880950866024212788997219294585937270... (see A048651, A048652).

Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Sep 17 2009: (Start)

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

contrast with:

1 = Sum_{n>=0} 2^(n*(n+1)/2) * x^n/[Product_{k=1..n+1} (1+2^k*x)]. (End)

A005329 := proc(n) option remember; if n=1 then 1 else (2^n-1)*A005329(n-1); fi; end;

restart:with (combinat):a:=n->mul(stirling2(j, 2), j=2..n): seq(a(n), n=1..19); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 01 2009]

restart:a:= proc(n) option remember; if n=0 then 1 else add(binomial (n, j)*a(n-1), j=0..n-1) fi end: seq (a(n), n=0..14); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 29 2009]

(PARI) {a(n)=polcoeff(sum(m=0, n, 2^(m*(m+1)/2)*x^m/prod(k=0, m, 1+2^k*x+x*O(x^n))), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 17 2009]

Cf. A006125, A114604.

Cf. A005321.

Cf. A006088, A028362. [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 17 2009]

Adjacent sequences: A005326 A005327 A005328 this_sequence A005330 A005331 A005332

Sequence in context: A000681 A055555 A158888 this_sequence A134528 A118410 A125054

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Olivier Gerard 8/97.