cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A055883 Exponential transform of Pascal's triangle A007318.

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%I A055883 #18 Apr 09 2025 16:45:21
%S A055883 1,1,1,2,4,2,5,15,15,5,15,60,90,60,15,52,260,520,520,260,52,203,1218,
%T A055883 3045,4060,3045,1218,203,877,6139,18417,30695,30695,18417,6139,877,
%U A055883 4140,33120,115920,231840,289800,231840,115920,33120,4140,21147
%N A055883 Exponential transform of Pascal's triangle A007318.
%C A055883 Triangle T(n,k), 0 <= k <= n, read by rows, given by [1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, ...] DELTA [1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, ...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Aug 10 2005
%H A055883 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A055883 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F A055883 a(n,k) = Bell(n)*C(n,k).
%F A055883 E.g.f.: A(x,y) = exp(exp(x+xy)-1).
%e A055883    1;
%e A055883    1,  1;
%e A055883    2,  4,  2;
%e A055883    5, 15, 15,  5;
%e A055883   15, 60, 90, 60, 15;
%e A055883   ...
%t A055883 T[ n_, k_] := Binomial[n, k] * BellB[n]; (* _Michael Somos_, Apr 09 2025 *)
%o A055883 (PARI) T(n, k) = binomial(n, k) * sum(j=0, n, stirling(n, j, 2)); /* _Michael Somos_, Apr 09 2025 */
%Y A055883 Cf. A000110, A007318, A056860.
%Y A055883 Row sums give A055882.
%K A055883 nonn,tabl
%O A055883 0,4
%A A055883 _Christian G. Bower_, Jun 09 2000