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A349292 G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(x)^6)). 11
1, 2, 15, 190, 2871, 47643, 838888, 15389452, 290951545, 5629024955, 110908062511, 2217739684483, 44891645810124, 918086053852234, 18941156419798530, 393742848618632760, 8239112912485293357, 173406208518520952066, 3668419587671991125142 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} binomial(n+5*k,6*k) * binomial(7*k,k) / (6*k+1).
a(n) ~ sqrt(1 + 5*r) / (2 * 7^(2/3) * sqrt(3*Pi*(1-r)) * n^(3/2) * r^(n + 1/6)), where r = 0.043408935906208378827553096713877784793679356... is the root of the equation 7^7 * r = 6^6 * (1-r)^6. - Vaclav Kotesovec, Nov 14 2021
MATHEMATICA
nmax = 18; A[_] = 0; Do[A[x_] = 1/((1 - x) (1 - x A[x]^6)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Table[Sum[Binomial[n + 5 k, 6 k] Binomial[7 k, k]/(6 k + 1), {k, 0, n}], {n, 0, 18}]
CROSSREFS
Sequence in context: A208402 A098343 A052819 * A328121 A127090 A198522
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 13 2021
STATUS
approved

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Last modified April 19 19:02 EDT 2024. Contains 371798 sequences. (Running on oeis4.)