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A226739 Row 4 of array in A226513. 4
1, 5, 35, 305, 3155, 37625, 507035, 7608305, 125687555, 2265230825, 44210200235, 928594230305, 20880079975955, 500343586672025, 12726718227077435, 342425052939060305, 9715738272696568355, 289901469137229041225, 9074304882434034258635, 297297854264669632338305 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

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

FORMULA

E.g.f.: 1/(2 - exp(x))^5 (see the Ahlbach et al. paper, Theorem 4).

a(n) = Sum_{i=0..n} S2(n,i)*i!*binomial(4+i,i), where S2 is the Stirling number of the second kind (see the Ahlbach et al. paper, Theorem 3).

G.f.: 1/Q(0), where Q(k) = 1 - x*(3*k + 1 + m) - 2*x^2*(k + 1)*(k + 1 + m)/Q(k+1), m = 4 is row 4 of array in A226513; (continued fraction). - Sergei N. Gladkovskii, Oct 03 2013

MATHEMATICA

Range[0, 20]! CoefficientList[Series[(2 - Exp@x)^-5, {x, 0, 20}], x]

PROG

(MAGMA) m:=4; [&+[StirlingSecond(n, i)*Factorial(i)*Binomial(m+i, i): i in [0..n]]: n in [0..20]];

CROSSREFS

Cf. rows 0, 1, 2, 3 and 5 of A226513: A000670, A005649, A226515, A226738, A226740.

Sequence in context: A177354 A253096 A305964 * A109253 A052797 A225177

Adjacent sequences:  A226736 A226737 A226738 * A226740 A226741 A226742

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Jun 18 2013

STATUS

approved

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Last modified November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)