A340259 a(n) = A340312(n, 2^(n-1)). a(n) is the central term of row n of A340312.

1, 0, 14, 870, 18796230, 28634752793916486, 187118328452563149209991044344449606, 22533823529098462258163079522899558179092788838542277982316450977506091590

Offset

1,3

Comments

a(9) = 2299131884087642202247291403507120751687796592498104258 * C, where C is a composite factor with 96 digits.

C = P47*P49, with P47 = 88967307877356450624418823383132738084943851019 and

P49 = 4512180962860489443011495305279720577473472225641. - Hugo Pfoertner, Jan 09 2021

Links

Andrew Howroyd, Table of n, a(n) for n = 1..11

Formula

a(n) = (2*binomial(2^n-1, 2^(n-1)) + (2^n-1)*binomial(2^(n-1), 2^(n-2)))/2^n for n >= 3. - Andrew Howroyd, Jan 09 2021

Maple

seq(A340312_row(n)[2^(n-1)+1], n = 1..8);

Prog

(PARI) a(n) = {if(n<=2, n==1, (2*binomial(2^n-1, 2^(n-1)) + (2^n-1)*binomial(2^(n-1), 2^(n-2)))/2^n)} \\ Andrew Howroyd, Jan 09 2021

Crossrefs

Cf. A340312, A340263.

Sequence in context: A269335 A159871 A362998 * A269610 A115458 A241801

Adjacent sequences: A340256 A340257 A340258 * A340260 A340261 A340262

Keyword

nonn

Author

Peter Luschny, Jan 06 2021

Status

approved