A292629 a(n) = n! * [x^n] exp(n*x)*BesselI(1,2*x).

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

Seiichi Manyama, Table of n, a(n) for n = 0..386

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.

Cf. A138364, A186925.

Sequence in context: A348708 A379190 A307905 * A362700 A088794 A239841

Adjacent sequences: A292626 A292627 A292628 * A292630 A292631 A292632

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 20 2017

Status

approved