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A047990 a(n+1) = a(n) + (n^2 + 1)*a(n-1). 2
1, 2, 4, 14, 54, 292, 1696, 12500, 97300, 909800, 8888400, 100778200, 1185163000, 15798002000, 217275712000, 3329482106000, 52433793018000, 908110694260000, 16113910669480000, 311249886303980000, 6144485548655740000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
Studied by M. Bhargava (bhargava(AT)math.Princeton.EDU) and H. S. Wilf.
LINKS
FORMULA
a(n) ~ c * n!, where c = sqrt(Pi) * (1/(Gamma(1/2 + i/2) * Gamma(1 - i/2)) + 1/(Gamma(1/2 - i/2) * Gamma(1 + i/2)))/2 + hypergeom([1 - i, 1 - i], [2], -1) / 2^i = 2.6068398732089369139523868268495087173767147472699250704975984714... and i is the imaginary unit. - Vaclav Kotesovec, Sep 26 2021
MATHEMATICA
RecurrenceTable[{a[0]==1, a[1]==2, a[n]==a[n-1]+((n-1)^2+1)a[n-2]}, a, {n, 20}] (* Harvey P. Dale, May 07 2013 *)
CROSSREFS
Cf. A047991.
Sequence in context: A322859 A183949 A131180 * A000939 A367558 A109154
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved

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Last modified July 21 18:17 EDT 2024. Contains 374475 sequences. (Running on oeis4.)