A305627 a(n) = (2^n / n!) * (2^1 - 1) * (2^2 - 1) * ... * (2^n - 1).

1, 2, 6, 28, 210, 2604, 54684, 1984248, 126495810, 14364301980, 2938936185108, 1093818612893832, 746531203300040340, 940744167112404680760, 2201744527114646554984440, 9619275055995416488956686064, 78799898849332452450472052650530

Offset

0,2

Comments

a(n) = b[n, 0, 1] in A157285.

Links

G. C. Greubel, Table of n, a(n) for n = 0..85

Formula

0 = +a(n)*(+a(n+1)*(+2*a(n+3)) +a(n+2)*(-6*a(n+2) +a(n+3))) +a(n+1)*(+a(n+1)*(+4*a(n+2) - 4*a(n+3)) +a(n+2)*(+4*a(n+2))) for all n in Z.

Mathematica

a[ n_] := If[n < 0, 0, QPochhammer[2, 2, n] (-2)^n / n!];

Prog

(PARI) {a(n) = if( n<0, 0, prod(k=1, n, 2^k - 1) * 2^n / n!)};
(Magma) [1] cat [(&*[(2*k-1): k in [1..n]])*2^n/Factorial(n): n in [1..20]]; // G. C. Greubel, Jul 28 2018

Crossrefs

Cf. A157285.

Sequence in context: A125812 A093657 A355064 * A006117 A118025 A226773

Adjacent sequences: A305624 A305625 A305626 * A305628 A305629 A305630

Keyword

nonn,easy

Author

Michael Somos, Jun 06 2018

Status

approved