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A300872 a(n) = A300871(n) / (n*(n+1)/2). 2
1, 1, 8, 151, 4752, 214848, 12915744, 986580860, 92994888960, 10595684332288, 1436363905680384, 228679178713630208, 42284602089642237952, 8992606241049735405568, 2180532527491138011131904, 598191016068264518151780096, 184370870332464252513762869248, 63445183762362816656030378164224, 24238363163428954774170892697075712 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

It is conjectured that this sequence consists entirely of integers.

O.g.f. G(x) of A300871 satisfies: [x^n] exp( n*(n+1) * G(x) ) = n*(n+1) * [x^(n-1)] exp( n*(n+1) * G(x) ) for n>=1.

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..200

PROG

(PARI) {a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^((#A-1)*(#A))); A[#A] = ((#A-1)*(#A)*V[#A-1] - V[#A])/(#A-1)/(#A) ); (1/(n*(n+1)/2))*polcoeff( log(Ser(A)), n)}

for(n=1, 20, print1(a(n), ", "))

CROSSREFS

Cf. A300871.

Sequence in context: A302063 A220559 A264642 * A217502 A229955 A249481

Adjacent sequences:  A300869 A300870 A300871 * A300873 A300874 A300875

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 14 2018

STATUS

approved

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)