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A223528
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Triangle S(n,k) by rows: coefficients of 4^(n/2)*(x^(3/4)*d/dx)^n when n=0,2,4,6,...
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0
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1, 1, 4, 5, 40, 16, 45, 540, 432, 64, 585, 9360, 11232, 3328, 256, 9945, 198900, 318240, 141440, 21760, 1024, 208845, 5012280, 10024560, 5940480, 1370880, 129024, 4096, 5221125, 146191500, 350859600, 259896000, 79968000, 11289600, 716800, 16384, 151412625
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OFFSET
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1,3
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LINKS
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EXAMPLE
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Triangle begins:
1;
1, 4;
5, 40, 16;
45, 540, 432, 64;
585, 9360, 11232, 3328, 256;
9945, 198900, 318240, 141440, 21760, 1024;
208845, 5012280, 10024560, 5940480, 1370880, 129024, 4096;
5221125, 146191500, 350859600, 259896000, 79968000, 11289600, 716800, 16384;
151412625, 4845204000, 13566571200, 12059174400, 4638144000, 873062400, 83148800, 3801088, 65536;
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MAPLE
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a[0]:= f(x):
for i from 1 to 20 do
a[i] := simplify(4^((i+1)mod 2)*x^((2((i+1)mod 2)+1)/4)*(diff(a[i-1], x$1 )));
end do:
for j from 1 to 10 do
b[j]:=a[2j];
end do;
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CROSSREFS
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Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.
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KEYWORD
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AUTHOR
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STATUS
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approved
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