A047990 a(n+1) = a(n) + (n^2 + 1)*a(n-1).

1, 2, 4, 14, 54, 292, 1696, 12500, 97300, 909800, 8888400, 100778200, 1185163000, 15798002000, 217275712000, 3329482106000, 52433793018000, 908110694260000, 16113910669480000, 311249886303980000, 6144485548655740000

Offset

0,2

References

Studied by M. Bhargava (bhargava(AT)math.Princeton.EDU) and H. S. Wilf.

Links

T. D. Noe, Table of n, a(n) for n=0..100

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

Adjacent sequences: A047987 A047988 A047989 * A047991 A047992 A047993

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved