A047793
a(n) = Sum_{k=0..n} |Stirling1(n,k)*Stirling2(n,k)|.
Original entry on oeis.org
1, 1, 2, 12, 120, 1750, 34615, 882868, 28008694, 1076404824, 49100939538, 2615329877358, 160486317081673, 11218516998346216, 884855465842682269, 78106000651400369100, 7660758993518625156050, 829683453926089044978468
Offset: 0
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List([0..20], n-> Sum([0..n], k-> Stirling1(n,k)*Stirling2(n,k) )); # G. C. Greubel, Aug 07 2019
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[(&+[(-1)^(n-k)*StirlingFirst(n,k)*StirlingSecond(n,k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 07 2019
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seq(add((-1)^(n-k)*stirling1(n, k)*stirling2(n, k), k = 0..n), n = 0.. 20); # G. C. Greubel, Aug 07 2019
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Table[Sum[Abs[StirlingS1[n,k]StirlingS2[n,k]],{k,0,n}],{n,0,20}] (* Harvey P. Dale, Jul 18 2017 *)
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makelist(sum(abs(stirling1(n,k))*stirling2(n,k),k,0,n),n,0,12); /* Emanuele Munarini, Jul 01 2011 */
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{a(n) = sum(k=0,n, (-1)^(n-k)*stirling(n,k,1)*stirling(n,k,2))};
vector(20, n, n--; a(n)) \\ G. C. Greubel, Aug 07 2019
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[sum(stirling_number1(n,k)*stirling_number2(n,k) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 07 2019
A047794
a(n) = Sum_{k=0..n} C(n,k)*|Stirling1(n,k)*Stirling2(n,k)|.
Original entry on oeis.org
1, 1, 3, 34, 631, 16871, 617356, 28968990, 1680536159, 117572734195, 9715771690081, 932711356031016, 102653506699902874, 12810868034079756421, 1795954763065584594656, 280569433733767673934426, 48506369621902094002862671, 9224242346164172284054561019
Offset: 0
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List([0..20], n-> Sum([0..n], k-> Stirling1(n,k)*Stirling2(n,k) *Binomial(n,k) )); # G. C. Greubel, Aug 07 2019
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[(&+[(-1)^(n-k)*StirlingFirst(n,k)*StirlingSecond(n,k) *Binomial(n,k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 07 2019
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seq(add((-1)^(n-k)*binomial(n, k)*stirling1(n, k)*stirling2(n, k), k = 0 .. n), n = 0..20); # G. C. Greubel, Aug 07 2019
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Table[Sum[Binomial[n,k]Abs[StirlingS1[n,k]StirlingS2[n,k]],{k,0,n}],{n,0,20}] (* Harvey P. Dale, Apr 10 2012 *)
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{a(n) = sum(k=0,n, (-1)^(n-k)*stirling(n,k,1)*stirling(n,k,2) *binomial(n,k))};
vector(20, n, n--; a(n)) \\ G. C. Greubel, Aug 07 2019
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[sum(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
A047795
a(n) = Sum_{k=0..n} C(n,k)*Stirling1(n,k)*Stirling2(n,k).
Original entry on oeis.org
1, 1, -1, -20, 295, 871, -196784, 6287772, 29169631, -18200393741, 1304183716981, -27109895360074, -6212943553813622, 1062831339757496245, -85292203894284124100, -1487854700305245210924, 1896933688279584387159631, -377233175400513002923379973
Offset: 0
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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
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[(&+[StirlingFirst(n,k)*StirlingSecond(n,k)*Binomial(n,k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 07 2019
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seq(add(binomial(n,k)*stirling1(n,k)*stirling2(n, k), k = 0..n), n = 0 .. 20); # G. C. Greubel, Aug 07 2019
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Table[Sum[Binomial[n, k]*StirlingS1[n, k]*StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* G. C. Greubel, Aug 07 2019 *)
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{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
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[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
A382794
a(n) = Sum_{k=0..n} Stirling1(n,k) * Stirling2(n,k) * (k!)^2.
Original entry on oeis.org
1, 1, 3, 2, -418, -14676, -234344, 18565056, 2659703616, 169046742960, -6539356064736, -4061128974843744, -672969012637199040, -19289566159655581440, 27323548725052131528960, 10157639436460221570630144, 1433264952547826545065237504, -520046813680980959472490690560
Offset: 0
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Table[Sum[StirlingS1[n, k] StirlingS2[n, k] (k!)^2, {k, 0, n}], {n, 0, 17}]
Table[(n!)^2 SeriesCoefficient[1/(1 - (Exp[x] - 1) Log[1 + y]), {x, 0, n}, {y, 0, n}], {n, 0, 17}]
Showing 1-4 of 4 results.