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.
%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