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A370381
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Array read by antidiagonals: A(n,k) = Sum_{j=0..k+1} binomial(k+2, j+1)*A(n-1,j) with A(0,k) = 1, n >= 0, k >= 0.
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1
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1, 1, 3, 1, 7, 13, 1, 15, 45, 71, 1, 31, 145, 319, 461, 1, 63, 453, 1355, 2525, 3447, 1, 127, 1393, 5623, 13241, 22199, 29093, 1, 255, 4245, 23051, 68261, 138219, 215157, 273343, 1, 511, 12865, 93799, 348761, 850031, 1549889, 2282639, 2829325, 1, 1023, 38853
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OFFSET
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0,3
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LINKS
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EXAMPLE
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Array begins:
==================================================
n\k| 0 1 2 3 4 5 ...
---+----------------------------------------------
0 | 1 1 1 1 1 1 ...
1 | 3 7 15 31 63 127 ...
2 | 13 45 145 453 1393 4245 ...
3 | 71 319 1355 5623 23051 93799 ...
4 | 461 2525 13241 68261 348761 1771925 ...
5 | 3447 22199 138219 850031 5193867 31604159 ...
...
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PROG
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(PARI)
A(m, n=m)={my(r=vectorv(m+1), v=vector(n+m+1, k, 1)); r[1] = v[1..n+1];
for(i=1, m, v=vector(#v-1, k, sum(j=1, k+1, binomial(k+1, j)*v[j])); r[1+i] = v[1..n+1]); Mat(r)}
{ A(5) }
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CROSSREFS
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Column k=0 is A003319 (without pair of initial terms and with different offset).
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KEYWORD
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AUTHOR
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STATUS
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approved
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