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A182422 a(n) = Sum_{k = 0..n} C(n,k)^8. 5
1, 2, 258, 13124, 1810690, 200781252, 30729140484, 4579408029576, 770670360699138, 132018919625044100, 23913739057463037508, 4433505541977804821256, 848185646293853978499844, 165563367990287610967653512, 32993144260428865295508700680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Vaclav Kotesovec, Recurrence (of order 4)

FORMULA

Asymptotic (p = 8): a(n) ~ 2^(p*n)/sqrt(p)*(2/(Pi*n))^((p - 1)/2)*( 1 - (p - 1)^2/(4*p*n) + O(1/n^2) ).

For r a nonnegative integer, Sum_{k = r..n} C(k,r)^8*C(n,k)^8 = C(n,r)^8*a(n-r), where we take a(n) = 0 for n < 0. - Peter Bala, Jul 27 2016

MAPLE

a := n -> hypergeom([seq(-n, i=1..8)], [seq(1, i=1..7)], 1):

seq(simplify(a(n)), n=0..14); # Peter Luschny, Jul 27 2016

MATHEMATICA

Table[Total[Binomial[n, Range[0, n]]^8], {n, 0, 20}] (* T. D. Noe, Apr 28 2012 *)

CROSSREFS

Cf. A000079, A000984, A000172, A005260, A005261, A069865, A182421.

Sequence in context: A327777 A196288 A128697 * A218435 A089663 A252708

Adjacent sequences:  A182419 A182420 A182421 * A182423 A182424 A182425

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Apr 28 2012

STATUS

approved

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Last modified February 23 06:13 EST 2020. Contains 332159 sequences. (Running on oeis4.)