A292630 - OEIS

A292630

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(0,2*x) + BesselI(1,2*x)).

1, 1, 1, 1, 2, 2, 1, 3, 5, 3, 1, 4, 10, 13, 6, 1, 5, 17, 35, 35, 10, 1, 6, 26, 75, 126, 96, 20, 1, 7, 37, 139, 339, 462, 267, 35, 1, 8, 50, 233, 758, 1558, 1716, 750, 70, 1, 9, 65, 363, 1491, 4194, 7247, 6435, 2123, 126, 1, 10, 82, 535, 2670, 9660, 23460, 34016, 24310, 6046, 252, 1, 11, 101, 755, 4451, 19846, 63195, 132339, 160795, 92378, 17303, 462

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OFFSET

0,5

COMMENTS

A(n,k) is the k-th binomial transform of A001405 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(0,2*x) + BesselI(1,2*x)).

EXAMPLE

E.g.f. of column k: A_k(x) = 1 + (k + 1)*x/1! + (k^2 + 2*k + 2)*x^2/2! + (k^3 + 3*k^2 + 6*k + 3)*x^3/3! + (k^4 + 4*k^3 + 12*k^2 + 12*k + 6)*x^4/4! + ...

Square array begins:

1, 1, 1, 1, 1, 1, ...

1, 2, 3, 4, 5, 6, ...

2, 5, 10, 17, 26, 37, ...

3, 13, 35, 75, 139, 233, ...

6, 35, 126, 339, 758, 1491, ...

10, 96, 462, 1558, 4194, 9660, ...

MAPLE

[seq(seq((k)!*add((m-j)^(j-i)/floor(i/2)!/ceil(i/2)!/(j-i)!, i=0..j), j=0..m), m=0..20)]; # Robert Israel, Sep 20 2017

MATHEMATICA

Table[Function[k, n! SeriesCoefficient[Exp[k x] (BesselI[0, 2 x] + BesselI[1, 2 x]), {x, 0, n}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten

CROSSREFS

Columns k=0..5 give A001405, A005773 (with first term deleted), A001700, A026378 (with offset 0), A005573, A122898.

Main diagonal gives A292631.

Sequence in context: A073133 A106179 A081572 * A144287 A106196 A037027

Adjacent sequences: A292627 A292628 A292629 * A292631 A292632 A292633

KEYWORD

nonn,tabl

AUTHOR

Ilya Gutkovskiy, Sep 20 2017

STATUS

approved