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.

A047795 a(n) = Sum_{k=0..n} C(n,k)*Stirling1(n,k)*Stirling2(n,k).

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%I A047795 #12 Sep 08 2022 08:44:57
%S A047795 1,1,-1,-20,295,871,-196784,6287772,29169631,-18200393741,
%T A047795 1304183716981,-27109895360074,-6212943553813622,1062831339757496245,
%U A047795 -85292203894284124100,-1487854700305245210924,1896933688279584387159631,-377233175400513002923379973
%N A047795 a(n) = Sum_{k=0..n} C(n,k)*Stirling1(n,k)*Stirling2(n,k).
%H A047795 G. C. Greubel, <a href="/A047795/b047795.txt">Table of n, a(n) for n = 0..280</a>
%p A047795 seq(add(binomial(n,k)*stirling1(n,k)*stirling2(n, k), k = 0..n), n = 0 .. 20); # _G. C. Greubel_, Aug 07 2019
%t A047795 Table[Sum[Binomial[n, k]*StirlingS1[n, k]*StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* _G. C. Greubel_, Aug 07 2019 *)
%o A047795 (PARI) {a(n) = sum(k=0,n,stirling(n,k,1)*stirling(n,k,2)*binomial(n,k))};
%o A047795 vector(20, n, n--; a(n)) \\ _G. C. Greubel_, Aug 07 2019
%o A047795 (Magma) [(&+[StirlingFirst(n,k)*StirlingSecond(n,k)*Binomial(n,k): k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Aug 07 2019
%o A047795 (Sage) [sum((-1)^(n-k)*stirling_number1(n,k)* stirling_number2(n,k) *binomial(n,k) for k in (0..n)) for n in (0..20)] # _G. C. Greubel_, Aug 07 2019
%o A047795 (GAP) List([0..20], n-> Sum([0..n], k-> (-1)^(n-k)*Stirling1(n,k) *Stirling2(n,k)*Binomial(n,k) )); # _G. C. Greubel_, Aug 07 2019
%Y A047795 Cf. A008275, A008277, A047792, A047793, A047794.
%K A047795 sign
%O A047795 0,4
%A A047795 _N. J. A. Sloane_