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A156266
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a(n) = 7^n*Catalan(n).
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7
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1, 7, 98, 1715, 33614, 705894, 15529668, 353299947, 8243665430, 196199237234, 4744454282204, 116239129913998, 2879153833254412, 71978845831360300, 1813866914950279560, 46026872966863343835, 1175038992212864189670
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) is the upper left term in M^n, M = an infinite square production matrix:
7, 7, 0, 0, 0, 0, ...
7, 7, 7, 0, 0, 0, ...
7, 7, 7, 7, 0, 0, ...
7, 7, 7, 7, 7, 0, ...
... (End)
G.f.: 1/(1 - 7*x/(1 - 7*x/(1 - 7*x/(1 - ...)))), a continued fraction. - Ilya Gutkovskiy, Aug 08 2017
Sum_{n>=0} 1/a(n) = 266/243 + 392*arctan(1/(3*sqrt(3))) / (729*sqrt(3)). - Vaclav Kotesovec, Nov 23 2021
Sum_{n>=0} (-1)^n/a(n) = 770/841 - 1176*arctanh(1/sqrt(29)) / (841*sqrt(29)). - Amiram Eldar, Jan 25 2022
D-finite with recurrence (n+1)*a(n) +14*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Mar 21 2022
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MAPLE
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A156266_list := proc(n) local j, a, w; a := array(0..n); a[0] := 1;
for w from 1 to n do a[w] := 7*(a[w-1]+add(a[j]*a[w-j-1], j=1..w-1)) od; convert(a, list)end: A156266_list(16); # Peter Luschny, May 19 2011
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MATHEMATICA
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Table[7^n * CatalanNumber[n], {n, 0, 16}] (* Amiram Eldar, Jan 25 2022 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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