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A304936 a(n) = [x^n] 1/(1 - n*x/(1 - x - n*x/(1 - x - n*x/(1 - x - n*x/(1 - x - n*x/(1 - ...)))))), a continued fraction. 0
1, 1, 10, 183, 5076, 191105, 9140118, 531731935, 36496595656, 2889768574449, 259443165181410, 26054614893427703, 2894791106297891100, 352618782117325104849, 46736101530152250554926, 6696645353339606889836415, 1031600569146491935984293648, 170029083604373881344301895585 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = [x^n] 2/(1 + x + sqrt(1 - x*(2 + 4*n - x))).

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

MATHEMATICA

Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-n x, 1 - x, {i, 1, n}]), {x, 0, n}], {n, 0, 17}]

Table[SeriesCoefficient[2/(1 + x + Sqrt[1 - x (2 + 4 n - x)]), {x, 0, n}], {n, 0, 17}]

Table[Sum[(-1)^(n - k) (n + 1)^k Binomial[n, k] Binomial[n + k, k]/(k + 1), {k, 0, n}], {n, 0, 17}]

Table[(-1)^n Hypergeometric2F1[-n, n + 1, 2, n + 1], {n, 0, 17}]

CROSSREFS

Cf. A001003, A107841, A131763, A131765, A131846, A131869, A131926, A131927, A292798.

Sequence in context: A064092 A171513 A240405 * A239764 A179521 A211102

Adjacent sequences:  A304933 A304934 A304935 * A304937 A304938 A304939

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 21 2018

STATUS

approved

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)