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A226741
Column 4 of array in A226513.
4
75, 308, 807, 1704, 3155, 5340, 8463, 12752, 18459, 25860, 35255, 46968, 61347, 78764, 99615, 124320, 153323, 187092, 226119, 270920, 322035, 380028, 445487, 519024, 601275, 692900, 794583, 907032, 1030979, 1167180, 1316415, 1479488, 1657227, 1850484
OFFSET
0,1
COMMENTS
This is the case h = 4 in Sum_{k=0..h} S2(h,k)*k!*binomial(n+k,k), where S2 is the Stirling number of the second kind (see the Ahlbach et al. paper, Theorem 3). [Bruno Berselli, Jun 20 2013]
LINKS
Connor Ahlbach, Jeremy Usatine and Nicholas Pippenger, Barred Preferential Arrangements, Electron. J. Combin., Volume 20, Issue 2 (2013), #P55.
FORMULA
G.f.: (75 - 67*x + 17*x^2 - x^3)/(1 - x)^5.
a(n) = (n + 1)^4 + 12*(n + 1)^3 + 36*(n + 1)^2 + 26*(n + 1).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
E.g.f.: exp(x)*(75 + 233*x + 133*x^2 + 22*x^3 + x^4). - Franck Maminirina Ramaharo, Nov 29 2018
MATHEMATICA
Table[(n+1)^4 + 12 (n+1)^3 + 36 (n+1)^2 + 26 (n+1), {n, 0, 40}] (* or *) CoefficientList[Series[(75 - 67 x + 17 x^2 - x^3) / (1 - x)^5, {x, 0, 40}], x]
PROG
(Magma) [(n+1)^4+12*(n+1)^3+36*(n+1)^2+26*(n+1): n in [0..35]] /* or */ I:=[75, 308, 807, 1704, 3155]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]];
CROSSREFS
Cf. columns 2, 3 and 5, 6 of A226513: A005563, A226514, A226800, A226801.
Sequence in context: A158742 A292313 A158765 * A223078 A055561 A350245
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jun 18 2013
STATUS
approved