The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A348857 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A348857

G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(2*x))).
(history; published version)

#7 by Vaclav Kotesovec at Tue Nov 02 09:49:30 EDT 2021

STATUS

editing

approved

#6 by Vaclav Kotesovec at Tue Nov 02 09:49:23 EDT 2021

FORMULA

a(n) ~ c * 2^(n*(n-1)/2), where c = 10.96416094535958612421479005398505892527943513193882801485045169159164... - Vaclav Kotesovec, Nov 02 2021

STATUS

proposed

editing

#5 by Ilya Gutkovskiy at Tue Nov 02 05:56:02 EDT 2021

STATUS

editing

proposed

#4 by Ilya Gutkovskiy at Tue Nov 02 05:31:33 EDT 2021

NAME

G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(2*x))).

#3 by Ilya Gutkovskiy at Tue Nov 02 04:54:17 EDT 2021

CROSSREFS

Cf. A007317, A015083, A348858, A348859.

#2 by Ilya Gutkovskiy at Tue Nov 02 04:46:25 EDT 2021

NAME

allocated for Ilya Gutkovskiy

G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(2*x)).

DATA

1, 2, 7, 44, 481, 9254, 326395, 21927776, 2874607189, 744650622170, 383510575423471, 393869218949592212, 807827718206737362889, 3311287802485779192925838, 27136007596894473408507305443, 444677773080105539125038867872456, 14572535437424416878539776253365375549

OFFSET

0,2

FORMULA

a(n) = 1 + Sum_{k=0..n-1} 2^k * a(k) * a(n-k-1).

MATHEMATICA

nmax = 16; A[_] = 0; Do[A[x_] = 1/((1 - x) (1 - x A[2 x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a[n_] := a[n] = 1 + Sum[2^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]

CROSSREFS

Cf. A007317, A015083.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Nov 02 2021

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Tue Nov 02 04:46:25 EDT 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved