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A127328
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Inverse binomial transform of A026641; binomial transform of A127361.
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2
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1, 0, 3, 3, 15, 30, 99, 252, 747, 2064, 5973, 16995, 49089, 141414, 409755, 1188243, 3455811, 10064952, 29368377, 85809681, 251067645, 735446106, 2156695533, 6330729438, 18600079221, 54693760680, 160951905819, 473984678037, 1396755865527, 4118553190254
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OFFSET
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0,3
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COMMENTS
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Hankel transform is 3^n.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Sum_{j=0..k} (-1)^(n+j)*binomial(k+j, j)*binomial(n, k). - G. C. Greubel, Apr 30 2019
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MATHEMATICA
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a[n_]:= Sum[(-1)^n*Sum[(-1)^j*Binomial[k+j, j], {j, 0, k}]*Binomial[n, k], {k, 0, n}]; Table[a[n], {n, 0, 30}] (* G. C. Greubel, Apr 30 2019 *)
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PROG
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(PARI) {a(n) = sum(k=0, n, sum(j=0, k, (-1)^(n+j)*binomial(k+j, j)* binomial(n, k)))}; \\ G. C. Greubel, Apr 30 2019
(Magma) [ (&+[ (&+[(-1)^(n+j)*Binomial(k+j, j)*Binomial(n, k): j in [0..k]]): k in [0..n]]) : n in [0..30]]; // G. C. Greubel, Apr 30 2019
(Sage) [sum(sum((-1)^(n+j)*binomial(k+j, j)*binomial(n, k) for j in (0..k)) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Apr 30 2019
(GAP) List([0..30], n-> Sum([0..n], k-> Sum([0..k], j-> (-1)^(n+j)* Binomial(k+j, j)*Binomial(n, k)))) # G. C. Greubel, Apr 30 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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