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A294117 a(n) = (n!)^2 * Sum_{k=1..n} binomial(n,k) / k^2. 1
1, 9, 139, 3460, 129076, 6831216, 492314544, 46810296576, 5724123883776, 881047053849600, 167511790501401600, 38685942660873830400, 10689310289146278297600, 3485920800452969462169600, 1325434521073620201431040000, 581241452210335678204477440000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..238

FORMULA

a(n) = (5*n^2 - 7*n + 3)*a(n-1) - (n-1)^2*(9*n^2 - 24*n + 17)*a(n-2) + (n-2)^3*(n-1)^2*(7*n - 13)*a(n-3) - 2*(n-3)^3*(n-2)^3*(n-1)^2*a(n-4).

a(n) ~ (n!)^2 * 2^(n+2) / n^2.

MAPLE

f:= gfun:-rectoproc({a(n) = (5*n^2 - 7*n + 3)*a(n-1) - (n-1)^2*(9*n^2 - 24*n + 17)*a(n-2) + (n-2)^3*(n-1)^2*(7*n - 13)*a(n-3) - 2*(n-3)^3*(n-2)^3*(n-1)^2*a(n-4), a(1)=1, a(2)=9, a(3)=139, a(4)=3460}, a(n), remember):

map(f, [$1..20]); # Robert Israel, Oct 23 2017

MATHEMATICA

Table[n!^2*Sum[Binomial[n, k]/k^2, {k, 1, n}], {n, 1, 20}]

Table[n!^2*n*HypergeometricPFQ[{1, 1, 1, 1 - n}, {2, 2, 2}, -1], {n, 1, 20}]

PROG

(MAGMA) I:=[1, 9, 139, 3460]; [n le 4 select I[n] else  (5*n^2- 7*n+3)*Self(n-1)-(n-1)^2*(9*n^2-24*n+17)*Self(n-2)+(n-2)^3*(n-1)^2*(7*n-13)*Self(n-3)-2*(n-3)^3*(n-2)^3*(n-1)^2*Self(n-4): n in [1..16]]; // Vincenzo Librandi, Oct 24 2017

CROSSREFS

Cf. A000424, A060237, A103213.

Sequence in context: A296394 A322576 A243673 * A266634 A092652 A137051

Adjacent sequences:  A294114 A294115 A294116 * A294118 A294119 A294120

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 23 2017

STATUS

approved

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Last modified November 29 12:16 EST 2020. Contains 338766 sequences. (Running on oeis4.)