A341106 - OEIS

A341106

a(n) = 2^n*E2poly(n, -1/2), where E2poly(n, x) = Sum_{k=0..n} A340556(n, k)*x^k, are the second-order Eulerian polynomials.

1, -1, 0, 6, -12, -144, 1080, 5184, -127008, 95904, 19077120, -154929024, -3210337152, 70284900096, 391453171200, -30354545511936, 153830450875392, 13189520200402944, -244127117929789440, -5109022268709986304, 237988748560571301888, 571783124036801765376

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..21.

MAPLE

E2poly := (n, x) -> add(A340556(n, k)*x^k, k = 0..n):

seq(2^n*E2poly(n, -1/2), n = 0..21);

# By series reversion:

serrev := proc(gf, len) series(gf, y, len);

gfun:-seriestoseries(%, 'revogf'); gfun:-seriestolist(%);

gfun:-listtolist(%, 'Laplace'); subsop(1 = NULL, %) end: