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A088927 Antidiagonal sums of table A088925, which lists coefficients T(n,k) of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/(1-x-y) + xy*f(x,y)^3. 3
1, 2, 5, 14, 43, 142, 496, 1808, 6807, 26270, 103357, 412942, 1670572, 6828824, 28159880, 116997296, 489271039, 2057800158, 8698624303, 36936288650, 157474552403, 673830974654, 2892864930292, 12457038200008, 53789813903620 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = sum(k=0, n, sum(i=0, k, C(n, 2i)*C(n-2i, k-i)*A001764(i) )), where A001764(i)=(3i)!/[i!(2i+1)! ] (from Michael Somos).
G.f. satisfies A(x) = 1/(1-2x) + x^2*A(x)^3.
a(n) ~ (2 + 3*sqrt(3)/2)^(n + 3/2) / (3^(7/4) * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Oct 10 2020
EXAMPLE
A(x) = 1/(1-2x) + x^2*A(x)^3 since 1/(1-2x) = 1 + 2x + 4x^2 + 8x^3 +... and x^2*A(x)^3 = 1x^2 + 6x^3 + 27x^4 + 110x^5 +...
MATHEMATICA
Table[Sum[Sum[Binomial[n, 2*i] * Binomial[n - 2*i, k - i] * (3*i)! / (i! * (2*i + 1)!), {i, 0, k}], {k, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Oct 10 2020 *)
CROSSREFS
Cf. A088925 (table), A088926 (diagonal), A001764.
Sequence in context: A126566 A112808 A369158 * A110489 A005425 A035349
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 23 2003
STATUS
approved

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Last modified February 29 19:20 EST 2024. Contains 370428 sequences. (Running on oeis4.)