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A292629
a(n) = n! * [x^n] exp(n*x)*BesselI(1,2*x).
5
0, 1, 4, 30, 304, 3885, 59976, 1085973, 22571200, 529712667, 13856212600, 399773871068, 12612288989664, 431948624278795, 15960564546516240, 632898895109081310, 26809122466181751552, 1208177444352064438155, 57719104861915100554200, 2913802658820378870546498, 154991214138728849712151200
OFFSET
0,3
COMMENTS
The n-th term of the n-th binomial transform of A138364.
LINKS
N. J. A. Sloane, Transforms
FORMULA
a(n) = A292628(n,n).
a(n) ~ BesselI(1,2) * n^n. - Vaclav Kotesovec, Sep 20 2017
a(n) = [x^(n-1)] (1+n*x+x^2)^n = [x^(n+1)] (1+n*x+x^2)^n. - Seiichi Manyama, May 01 2019
MATHEMATICA
Table[n!*SeriesCoefficient[E^(n*x)*BesselI[1, 2*x], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 20 2017 *)
PROG
(PARI) a(n) = polcoef((1+n*x+x^2)^n, n-1); \\ Michel Marcus, May 01 2019
CROSSREFS
Main diagonal of A292628.
Sequence in context: A052452 A348708 A307905 * A362700 A088794 A239841
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 20 2017
STATUS
approved