A181649 An INVERT sequence for A010054.

1, 1, 2, 3, 6, 10, 18, 32, 57, 101, 179, 319, 566, 1006, 1786, 3174, 5638, 10016, 17793, 31609, 56153, 99753, 177211, 314810, 559255, 993501, 1764935, 3135366, 5569909, 9894819, 17577926, 31226796, 55473705, 98547807, 175067983, 311004383

Offset

0,3

Comments

Eigensequence of the sequence array for A010054.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1/(1-x*Product{k>0,(1 - x^(2k))/(1-x^(2k-1))}).

G.f.: 1 / (1 - x / (1 - x / (1 + x / (1 + x^1 / (1 - x / (1 + x / (1 + x^2 / (1 - x / (1 + x / (1 + x^3 / (1 - x / (1 + x / ...)))))))))))). - Michael Somos, Jan 03 2013

a(n) ~ c / r^n, where r = 0.5629116358141452127351993944163442032777187438473224785071475357915... is the root of the equation (-1 + x)*QPochhammer(x^2, x^2) = QPochhammer(1/x, x^2) and c = 0.5730261147067572839709085685318242468812339379480160560847761872213851... - Vaclav Kotesovec, Jan 23 2024

Example

1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 10*x^5 + 18*x^6 + 32*x^7 + 57*x^8 + 101*x^9 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[1/(1 - q^(7/8)*eta[q^2]^2/eta[q]), {q, 0, 50}], q] (* G. C. Greubel, Sep 16 2018 *)

Prog

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( 1 / (1 - x * eta(x^2 + A)^2 / eta(x + A)), n))} /* Michael Somos, Jan 03 2013 */

Crossrefs

Sequence in context: A018073 A357451 A224342 * A052972 A018166 A144026

Adjacent sequences: A181646 A181647 A181648 * A181650 A181651 A181652

Keyword

easy,nonn

Author

Paul Barry, Nov 03 2010

Status

approved