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A295611 a(n) = Sum_{k=0..n} (-1)^k*binomial(n,k)^k. 2
1, 0, 0, 6, -30, -280, 35070, -2508268, -47103462, 241470400824, -256752145545390, 128291714550379292, 2203924344437376054780, -37693423679943326954848176, 485163732930867224220253809178, 27101025121379607823580070619517816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..75

Eric Weisstein's World of Mathematics, Binomial Sums

FORMULA

a(n) = Sum_{k=0..n} (-1)^k*A219206(n,k).

Limit n->infinity |a(n)|^(1/n^2) = r^(r^2/(1-2*r)) = 1.533628065110458582053143..., where r = A220359 = 0.70350607643066243096929661621777... is the real root of the equation (1-r)^(2*r-1) = r^(2*r). - Vaclav Kotesovec, Nov 25 2017

MATHEMATICA

Table[Sum[(-1)^k Binomial[n, k]^k, {k, 0, n}], {n, 0, 15}]

Table[Sum[(-1)^k (n!/(k! (n - k)!))^k, {k, 0, n}], {n, 0, 15}]

PROG

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n, k)^k); \\ Michel Marcus, Nov 25 2017

CROSSREFS

Cf. A167008, A167010, A219206.

Sequence in context: A066108 A205339 A215288 * A264641 A110374 A232978

Adjacent sequences:  A295608 A295609 A295610 * A295612 A295613 A295614

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Nov 24 2017

STATUS

approved

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Last modified November 30 13:47 EST 2021. Contains 349420 sequences. (Running on oeis4.)