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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 (list; graph; refs; listen; history; text; internal format)
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]] /* 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 A193252

Adjacent sequences:  A226738 A226739 A226740 * A226742 A226743 A226744

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jun 18 2013

STATUS

approved

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Last modified October 21 12:12 EDT 2019. Contains 328299 sequences. (Running on oeis4.)