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A047795
a(n) = Sum_{k=0..n} C(n,k)*Stirling1(n,k)*Stirling2(n,k).
4
1, 1, -1, -20, 295, 871, -196784, 6287772, 29169631, -18200393741, 1304183716981, -27109895360074, -6212943553813622, 1062831339757496245, -85292203894284124100, -1487854700305245210924, 1896933688279584387159631, -377233175400513002923379973
OFFSET
0,4
LINKS
MAPLE
seq(add(binomial(n, k)*stirling1(n, k)*stirling2(n, k), k = 0..n), n = 0 .. 20); # G. C. Greubel, Aug 07 2019
MATHEMATICA
Table[Sum[Binomial[n, k]*StirlingS1[n, k]*StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* G. C. Greubel, Aug 07 2019 *)
PROG
(PARI) {a(n) = sum(k=0, n, stirling(n, k, 1)*stirling(n, k, 2)*binomial(n, k))};
vector(20, n, n--; a(n)) \\ G. C. Greubel, Aug 07 2019
(Magma) [(&+[StirlingFirst(n, k)*StirlingSecond(n, k)*Binomial(n, k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 07 2019
(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
(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
CROSSREFS
KEYWORD
sign
STATUS
approved