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A287318 Square array A(n,k) = (2*n)! [x^n] BesselI(0, 2*sqrt(x))^k read by antidiagonals. 3
1, 1, 0, 1, 2, 0, 1, 4, 6, 0, 1, 6, 36, 20, 0, 1, 8, 90, 400, 70, 0, 1, 10, 168, 1860, 4900, 252, 0, 1, 12, 270, 5120, 44730, 63504, 924, 0, 1, 14, 396, 10900, 190120, 1172556, 853776, 3432, 0, 1, 16, 546, 19920, 551950, 7939008, 32496156, 11778624, 12870, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..54.

FORMULA

A(n,k) = A287316(n,k) * binomial(2*n,n).

EXAMPLE

Arrays start:

k\n| 0   1    2      3        4          5           6

---|---------------------------------------------------------

k=0| 1,  0,   0,     0,       0,         0,            0, ... A000007

k=1| 1,  2,   6,    20,      70,       252,          924, ... A000984

k=2| 1,  4,  36,   400,    4900,     63504,       853776, ... A002894

k=3| 1,  6,  90,  1860,   44730,   1172556,     32496156, ... A002896

k=4| 1,  8, 168,  5120,  190120,   7939008,    357713664, ... A039699

k=5| 1, 10, 270, 10900,  551950,  32232060,   2070891900, ... A287317

k=6| 1, 12, 396, 19920, 1281420,  96807312,   8175770064, ...

k=7| 1, 14, 546, 32900, 2570050, 238935564,  25142196156, ...

k=8| 1, 16, 720, 50560, 4649680, 514031616,  64941883776, ...

k=9| 1, 18, 918, 73620, 7792470, 999283068, 147563170524, ...

MAPLE

A287318_row := proc(k, len) local b, ser;

b := k -> BesselI(0, 2*sqrt(x))^k: ser := series(b(k), x, len);

seq((2*i)!*coeff(ser, x, i), i=0..len-1) end:

for k from 0 to 6 do A287318_row(k, 9) od;

MATHEMATICA

Table[Table[SeriesCoefficient[BesselI[0, 2 Sqrt[x]]^k, {x, 0, n}] (2 n)!, {n, 0, 6}], {k, 0, 6}]

CROSSREFS

Rows: A000007 (k=0), A000984 (k=1), A002894 (k=2), A002896 (k=3), A039699 (k=4), A287317 (k=5).

Columns: A005843 (n=1), A152746 (n=2), 20*A169711 (n=3), 70*A169712 (n=4), 252*A169713 (n=5).

Main diagonal gives A303503.

Cf. A287316.

Sequence in context: A229223 A128749 A106579 * A173003 A294411 A274390

Adjacent sequences:  A287315 A287316 A287317 * A287319 A287320 A287321

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, May 23 2017

STATUS

approved

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Last modified June 25 12:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)