A025013 Central octonomial coefficients: largest coefficient of (1+x+...+x^7)^n.

1, 1, 8, 48, 344, 2460, 18152, 134512, 1012664, 7635987, 58199208, 443658688, 3409213016, 26184550496, 202384723528, 1562970918720, 12133130451576, 94094281551304, 732910480638272, 5702603044247504, 44538031693977544

Offset

0,3

Comments

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

Links

T. D. Noe and Vaclav Kotesovec, Table of n, a(n) for n = 0..500 (first 200 terms from T. D. Noe)

Vaclav Kotesovec, Recurrence

Formula

a(n) ~ 8^n * sqrt(2/(21*Pi*n)). - Vaclav Kotesovec, Aug 09 2013

Mathematica

Flatten[{1, Table[Coefficient[Expand[Sum[x^j, {j, 0, 7}]^n], x^Floor[7*n/2]], {n, 1, 20}]}] (* Vaclav Kotesovec, Aug 09 2013 *)

Crossrefs

Cf. A001405, A002426, A005190, A005191, A018901, A025012, A025014.

Sequence in context: A203799 A095897 A220251 * A215706 A200161 A172111

Adjacent sequences: A025010 A025011 A025012 * A025014 A025015 A025016

Keyword

easy,nonn

Author

David W. Wilson

Status

approved