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A025014
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Central "nonomial" coefficient: largest coefficient of (1+x+...+x^8)^n.
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42
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1, 1, 9, 61, 489, 3951, 32661, 273127, 2306025, 19610233, 167729959, 1441383219, 12434998005, 107632809909, 934263293679, 8129320828911, 70886845397481, 619288973447049, 5419332253680705, 47494787636620701, 416800775902696839
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OFFSET
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0,3
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COMMENTS
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Generally, largest coefficient of (1+x+...+x^k)^n is asymptotic to (k+1)^n * sqrt(6/(k*(k+2)*Pi*n)). - Vaclav Kotesovec, Aug 09 2013
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REFERENCES
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Rudolph-Lilith, Michelle, and Lyle E. Muller. "On a link between Dirichlet kernels and central multinomial coefficients." Discrete Mathematics 338.9 (2015): 1567-1572.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
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FORMULA
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The Almkvist-Zeilberger algorithm in EKHAD establishes the following recurrence:
-6561*(4*n+17)*(4*n+13)*(5*n+24)*(5*n+19)*(5*n+14)*(5*n+23)*(n+4)*(n+3)*(n+2)*(n+1)*a(n)+1458*(5*n+24)*(5*n+19)*(4*n+17)*(5*n+9)*(4*n+9)*(5*n+18)*(2*n+9)*(n+4)*(
n+3)*(n+2)*a(n+1)+162*(5*n+24)*(5*n+14)*(4*n+13)*(5*n+23)*(n+4)*(n+3)*(1020*n^4+12291*n^3+53378*n^2+98617*n+65610)*a(n+2)-18*(4*n+17)*(4*n+9)*(5*n+19)*(2*n+9)*(5
*n+9)*(5*n+18)*(n+4)*(385*n^3+4158*n^2+14551*n+16610)*a(n+3)-(5*n+23)*(4*n+13)*(4*n+9)*(5*n+24)*(5*n+14)*(5*n+9)*(2101*n^4+33616*n^3+201391*n^2+535416*n+532980)*
a(n+4)+8*(4*n+19)*(5*n+19)*(5*n+14)*(5*n+9)*(2*n+9)*(4*n+17)*(4*n+13)*(4*n+9)*(5*n+18)*(n+5)*a(n+5) = 0. - Doron Zeilberger, Apr 02 2013.
a(n) ~ 9^n * sqrt(3/(40*Pi*n)). - Vaclav Kotesovec, Aug 09 2013
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MATHEMATICA
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Flatten[{1, Table[Coefficient[Expand[Sum[x^j, {j, 0, 8}]^n], x^(4*n)], {n, 1, 20}]}] (* Vaclav Kotesovec, Aug 09 2013 *)
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CROSSREFS
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Cf. A001405, A002426, A005190, A005191, A018901, A025012, A025013
Sequence in context: A162769 A126504 A361280 * A246567 A322086 A075139
Adjacent sequences: A025011 A025012 A025013 * A025015 A025016 A025017
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KEYWORD
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easy,nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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