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A020529
4th Bernoulli polynomial evaluated at powers of 2 (multiplied by 30).
1
-1, 119, 4319, 94079, 1727999, 29521919, 487710719, 7927726079, 127844351999, 2053539102719, 32920955781119, 527250311086079, 8440126636031999, 135075005485547519, 2161463946400235519, 34585534108092334079, 553385433841532927999, 8854302047907159736319
OFFSET
0,2
FORMULA
a(n) = 30*16^n - 60*8^n + 30*4^n - 1.
From Colin Barker, Aug 26 2016: (Start)
a(n) = 29*a(n-1) - 252*a(n-2) + 736*a(n-3) - 512*a(n-4) for n > 3.
G.f.: -(1 - 148*x - 616*x^2 + 448*x^3)/((1-x)*(1-4*x)*(1-8*x)*(1-16*x)). (End)
E.g.f.: exp(x)*(30*exp(3*x)*(exp(12*x) - 2*exp(4*x) + 1) - 1). - Elmo R. Oliveira, Sep 16 2024
MAPLE
seq(bernoulli(4, 2^i), i=0..24);
MATHEMATICA
LinearRecurrence[{29, -252, 736, -512}, {-1, 119, 4319, 94079}, 20] (* Harvey P. Dale, Feb 06 2020 *)
PROG
(PARI) Vec(-(1-148*x-616*x^2+448*x^3)/((1-x)*(1-4*x)*(1-8*x)*(1-16*x)) + O(x^20)) \\ Colin Barker, Aug 26 2016
CROSSREFS
Sequence in context: A156930 A263128 A048397 * A163006 A261686 A069328
KEYWORD
sign,easy
AUTHOR
STATUS
approved