A355414 Expansion of the e.g.f. log((1 - x) / (1 - 2*x)) / (1 - x)^5.

0, 1, 13, 149, 1750, 21894, 295500, 4320420, 68487120, 1176564240, 21883528800, 440117949600, 9557404012800, 223720054790400, 5634130146624000, 152315974848038400, 4409413104676608000, 136318041562123008000, 4487618159996944896000, 156852415886275726848000, 5803748680475885432832000

Offset

0,3

Comments

Conjecture: For p prime, a(p) == -1 (mod p).

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n} (-1)^(k+1)*k!*A062140(n, k+1).

a(0) = 0, a(n) = n!*Sum_{k=1..n} A000332(n-k+4)*(2^k-1)/k.

a(n) = binomial(n+4, 5)*n!*hypergeom([1 - n, 1, 1], [2, 6], -1). - Peter Luschny, Jul 01 2022

D-finite with recurrence a(n) +(-4*n-5)*a(n-1) +(n+3)*(5*n-3)*a(n-2) -2*(n-2)*(n+3)*(n+2)*a(n-3)=0. - R. J. Mathar, Jul 27 2022

Maple

A355414 := proc(n)
    n!*binomial(n+4, 5)*hypergeom([1-n, 1, 1], [2, 6], -1) ;
    simplify(%) ;
end proc:
seq(A355414(n), n=0..40) ; # R. J. Mathar, Jul 27 2022

Crossrefs

Cf. A000332, A062140, A355171, A355372, A355407.

Sequence in context: A090667 A125448 A163148 * A345217 A185405 A051475

Adjacent sequences: A355411 A355412 A355413 * A355415 A355416 A355417

Keyword

nonn

Author

Mélika Tebni, Jul 01 2022

Status

approved