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A293295 a(n) = Sum_{k=1..n} (-1)^(n-k)*hypergeom([k, k-2-n], [], 1). 2
1, 5, 27, 142, 847, 5817, 45733, 405836, 4012701, 43733965, 520794991, 6726601050, 93651619867, 1398047697137, 22275111534537, 377278848390232, 6768744159489913, 128228860181918421, 2557808459478878851, 53585748788874537830, 1176328664895760953831 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..21.

FORMULA

a(n) = A292898(n, 2).

From Vaclav Kotesovec, Jul 05 2018: (Start)

Recurrence: (n^2 - 4*n + 5)*a(n) = (n^3 - 3*n^2 + 3*n + 2)*a(n-1) - (n-1)*(2*n - 3)*a(n-2) - (n^3 - 3*n^2 + 2*n + 1)*a(n-3) + (n^2 - 2*n + 2)*a(n-4).

a(n) ~ n * n!.

a(n) ~ sqrt(2*Pi) * n^(n + 3/2) / exp(n). (End)

MAPLE

A293295 := n -> add((-1)^(n-k)*hypergeom([k, k-2-n], [], 1), k=1..n):

seq(simplify(A293295(n)), n=1..20);

MATHEMATICA

Table[Sum[(-1)^(n-k)*HypergeometricPFQ[{k, k-2-n}, {}, 1], {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Jul 05 2018 *)

CROSSREFS

Cf. A003470 (n=0), A193464 (n=1), this sequence (n=2), A292898 (n>=0).

Sequence in context: A221673 A257061 A052225 * A015535 A026292 A100193

Adjacent sequences:  A293292 A293293 A293294 * A293296 A293297 A293298

KEYWORD

nonn,changed

AUTHOR

Peter Luschny, Oct 05 2017

STATUS

approved

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Last modified July 17 07:23 EDT 2018. Contains 312694 sequences. (Running on oeis4.)