A273198 a(n) = T(n,2) with T(n, m) = (m*n+1)! * Sum_{k=0..n}( 1/(m*k+1) * Sum_{j=0..m*k} (-1)^j*C(k,j)*j^(m*n) ).

1, -2, 296, -327984, 1363872384, -15198541159680, 372495898187043840, -17616182020373076940800, 1464370216956293433318604800, -199499758936277018742988067635200, 42181903584776412718275835664105472000, -13251216132203374725100642797337549799424000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..123

Formula

a(n) ~ (-1)^n * sqrt(Pi) * 2^(4*n) * n^(4*n + 1/2) / (sqrt(1-c) * exp(4*n) * c^n * (2-c)^(n-1)), where c = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599... . - Vaclav Kotesovec, Jun 26 2016

Mathematica

Flatten[{1, Table[(2*n + 1)! * Sum[1/(2*k + 1)*Sum[(-1)^j*Binomial[k, j]*j^(2*n), {j, 0, 2*k}], {k, 0, n}], {n, 1, 10}]}] (* Vaclav Kotesovec, Jun 26 2016 *)

Prog

(Sage)
def T(n, m): return factorial(m*n+1) * sum(1/(m*k+1)*sum((-1)^j*binomial(k, j)* j^(m*n) for j in (0..m*k)) for k in (0..n))
def a(n): return T(n, 2)
print([a(n) for n in (0..12)])

Crossrefs

Cf. A129814, A273196, A273197.

Sequence in context: A362517 A132518 A277126 * A359208 A199946 A142800

Adjacent sequences: A273195 A273196 A273197 * A273199 A273200 A273201

Keyword

sign

Author

Peter Luschny, Jun 26 2016

Status

approved