A226741 Column 4 of array in A226513.

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Connor Ahlbach, Jeremy Usatine and Nicholas Pippenger, Barred Preferential Arrangements, Electron. J. Combin., Volume 20, Issue 2 (2013), #P55.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

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]];
(Magma) 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

Adjacent sequences: A226738 A226739 A226740 * A226742 A226743 A226744

Keyword

nonn,easy

Author

Vincenzo Librandi, Jun 18 2013

Status

approved