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A226800 Column 5 of array in A226513. 4
541, 2612, 7803, 18424, 37625, 69516, 119287, 193328, 299349, 446500, 645491, 908712, 1250353, 1686524, 2235375, 2917216, 3754637, 4772628, 5998699, 7463000, 9198441, 11240812, 13628903, 16404624, 19613125, 23302916, 27525987, 32337928, 37798049, 43969500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This is the case h = 5 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 (6,-15,20,-15,6,-1).

FORMULA

G.f.: (541 - 634*x + 246*x^2 - 34*x^3 + x^4)/(1 - x)^6.

a(n) = (n + 1)*(n^4 + 24*n^3 + 186*n^2 + 554*n + 541).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

E.g.f.: exp(x)*(541 + 2071*x + 1560*x^2 + 385*x^3 + 35*x^4 + x^5). - Franck Maminirina Ramaharo, Nov 29 2018

MATHEMATICA

Table[(n + 1)^5 + 20 (n+1)^4 + 120 (n+1)^3 + 250 (n+1)^2 + 150 (n+1), {n, 0, 40}] (* or *) CoefficientList[Series[(541 - 634 x + 246 x^2 - 34 x^3 + x^4) / (1 - x)^6, {x, 0, 30}], x]

PROG

(Magma) [(n+1)^5+20*(n+1)^4+120*(n+1)^3+250*(n+1)^2+150*(n+1): n in [0..30]]; /* or */ I:=[541, 2612, 7803, 18424, 37625, 69516]; [n le 6 select I[n] else 6*Self(n-1)-15*Self(n-2)+20*Self(n-3)-15*Self(n-4)+6*Self(n-5)-Self(n-6): n in [1..30]];

CROSSREFS

Cf. columns 2, 3, 4 and 6 of A226513: A005563, A226514, A226741, A226801.

Sequence in context: A031937 A031921 A129932 * A320619 A218095 A293582

Adjacent sequences: A226797 A226798 A226799 * A226801 A226802 A226803

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jun 18 2013

STATUS

approved

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Last modified December 1 14:52 EST 2022. Contains 358468 sequences. (Running on oeis4.)