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A292628

Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. exp(k*x)*BesselI(1,2*x).

0, 0, 1, 0, 1, 0, 0, 1, 2, 3, 0, 1, 4, 6, 0, 0, 1, 6, 15, 16, 10, 0, 1, 8, 30, 56, 45, 0, 0, 1, 10, 51, 144, 210, 126, 35, 0, 1, 12, 78, 304, 685, 792, 357, 0, 0, 1, 14, 111, 560, 1770, 3258, 3003, 1016, 126, 0, 1, 16, 150, 936, 3885, 10224, 15533, 11440, 2907, 0, 0, 1, 18, 195, 1456, 7570, 26550, 58947, 74280, 43758, 8350, 462

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OFFSET

0,9

COMMENTS

A(n,k) is the k-th binomial transform of A138364 evaluated at n.

LINKS

Table of n, a(n) for n=0..77.

N. J. A. Sloane, Transforms

FORMULA

E.g.f. of column k: exp(k*x)*BesselI(1,2*x).

EXAMPLE

E.g.f. of column k: A_k(x) = x/1! + 2*k*x^2/2! + 3*(k^2 + 1)*x^3/3! + 4*k*(k^2 + 3)*x^4/4! + 5*(k^4 + 6*k^2 + 2)*x^5/5! + ...