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A211246
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Irregular triangle read by rows: numbers a_m(i) related to Bernoulli and Euler polynomials.
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1
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4, 3, 6, 8, 5, 5, 8, 19, 12, 7, 14, 7, 10, 34, 44, 16, 9, 27, 30, 9, 12, 53, 104, 85, 20, 11, 44, 77, 55, 11, 14, 76, 200, 259, 146, 24, 13, 65, 156, 182, 91, 13, 16, 103, 340, 606, 560, 231, 28, 15, 90, 275, 450, 378, 140, 15, 18, 134, 532, 1210, 1572, 1092, 344, 32
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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2,1
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COMMENTS
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See the Sun (2008) reference for the (complicated) precise definition.
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LINKS
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EXAMPLE
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Triangle begins:
4
3
6 8
5 5
8 19 12
7 14 7
10 34 44 16
9 27 30 9
12 53 104 85 20
11 44 77 55 11
14 76 200 259 146 24
...
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MATHEMATICA
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c[m_, i_] := Binomial[m-1-i, i] + 4 Binomial[m-i, i-1];
d[m_, i_] := Binomial[m-i, i] m/(m -i);
a[m_, i_] := If[EvenQ[m], c[m, i], d[m, i]];
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PROG
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(PARI)
c(m, i) = binomial(m-1-i, i) + 4*binomial(m-i, i-1);
d(m, i) = binomial(m-i, i)*m / (m-i);
a(m, i) = if ( m%2 == 0, c(m, i), d(m, i) );
for (m=1, 16, for (i=1, floor(m/2), print1( a(m, i), ", "))) \\ Hugo Pfoertner, Nov 01 2017
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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