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A151645 Number of permutations of 4 indistinguishable copies of 1..n with exactly 7 adjacent element pairs in decreasing order. 2
0, 0, 112, 15018688, 69830127680, 99825129369600, 79985306860607376, 46314409921814756480, 22045769335091544766944, 9274231983519733250418880, 3600979296578512256763795120, 1326029824370661243342378614592, 471290654822091236131899199410048 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

G. C. Greubel, Generating functions and recurrence

FORMULA

From G. C. Greubel, Sep 12 2022: (Start)

a(n) = Sum_{j=0..7} (-1)^j*binomial(4*n+1, j)*binomial(11-j, 4)^n.

G.f., e.g.f., and recurrence are in the file "Generating functions and recurrence". (End)

MATHEMATICA

Table[Sum[(-1)^j*Binomial[4*n+1, j]*Binomial[11-j, 4]^n, {j, 0, 7}], {n, 30}] (* G. C. Greubel, Sep 12 2022 *)

PROG

(Magma) [(&+[(-1)^j*Binomial(4*n+1, j)*Binomial(11-j, 4)^n: j in [0..7]]): n in [1..30]]; // G. C. Greubel, Sep 12 2022

(SageMath)

def A151645(n): return sum((-1)^j*binomial(4*n+1, j)*binomial(11-j, 4)^n for j in (0..7))

[A151645(n) for n in (1..30)] # G. C. Greubel, Sep 12 2022

CROSSREFS

Column k=7 of A236463.

Sequence in context: A180039 A261949 A159432 * A115486 A157885 A204377

Adjacent sequences: A151642 A151643 A151644 * A151646 A151647 A151648

KEYWORD

nonn

AUTHOR

R. H. Hardin, May 29 2009

EXTENSIONS

Terms a(8) and beyond from Andrew Howroyd, May 06 2020

STATUS

approved

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Last modified November 30 00:02 EST 2022. Contains 358431 sequences. (Running on oeis4.)