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A226801 Column 6 of array in A226513. 4
4683, 25988, 87135, 227304, 507035, 1014348, 1871583, 3242960, 5342859, 8444820, 12891263, 19103928, 27595035, 38979164, 53985855, 73472928, 98440523, 130045860, 169618719, 218677640, 278946843, 352373868, 441147935, 547719024, 674817675, 825475508 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This is the case h = 6 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 (7,-21,35,-35,21,-7,1).

FORMULA

G.f.: (4683 - 6793*x + 3562*x^2 - 798*x^3 + 67*x^4 - x^5) / (1-x)^7.

a(n) = (n + 1)*(n^5 + 35*n^4 + 430*n^3 + 2320*n^2 + 5525*n + 4683).

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

E.g.f.: exp(x)*(4683 + 21305*x + 19921*x^2 + 6530*x^3 + 890*x^4 + 51*x^5 + x^6). - Franck Maminirina Ramaharo, Nov 29 2018

MATHEMATICA

Table[(n + 1) (n^5 + 35 n^4 + 430 n^3 + 2320 n^2 + 5525 n + 4683), {n, 0, 40}] (* or *) CoefficientList[Series[(4683 - 6793 x + 3562 x^2 - 798 x^3 + 67 x^4 - x^5) / (1-x)^7, {x, 0, 30}], x]

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {4683, 25988, 87135, 227304, 507035, 1014348, 1871583}, 30] (* Harvey P. Dale, Apr 27 2014 *)

PROG

(MAGMA) [(n+1)*(n^5+35*n^4+430*n^3+2320*n^2+5525*n+4683): n in [0..35]]; /* or */ I:=[4683, 25988, 87135, 227304, 507035, 1014348, 1871583]; [n le 7 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..30]];

CROSSREFS

Cf. columns 2, 3, 4, 5 of A226513: A005563, A226514, A226741, A226800.

Sequence in context: A022244 A252382 A190131 * A320620 A218096 A293583

Adjacent sequences:  A226798 A226799 A226800 * A226802 A226803 A226804

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jun 20 2013

STATUS

approved

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Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)