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A144452 Antidiagonal expansion of the polynomials: f(x,n) = 1/(exp(t) - Sum_{i=1..n} t^i/i!). 0
1, 1, 0, 1, 0, -3, 1, 0, 0, -4, 1, 0, 0, -4, 25, 1, 0, 0, 0, -5, 114, 1, 0, 0, 0, -5, -6, -287, 1, 0, 0, 0, 0, -6, 133, -4152, 1, 0, 0, 0, 0, -6, -7, 552, -1647, 1, 0, 0, 0, 0, 0, -7, -8, 1629, 192230, 1, 0, 0, 0, 0, 0, -7, -8, 621, -12610, 807961, 1, 0, 0, 0, 0, 0, 0, -8, -9, 2510, -128579, -10164804, 1, 0, 0, 0, 0, 0, 0, -8, -9, -10, 7381 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Row sums are:

{1, 2, 3, 20, 125, 804, 4501, 36896, 362673, 3831560, 40591001, 467518248, 6106124713, 87661533764, 1323052370025}.

Triangle sequence rows last terms are:

Table[n!*a[[1]][[n]], {n, 1, 15}]

{1, 0, -3, -4, 25,114, -287, -4152, -1647, 192230, 807961, -10164804, -111209111, 454840554, 14657978385}

LINKS

Table of n, a(n) for n=1..89.

FORMULA

f(x,n) = 1/(exp(t) - Sum_{i=1..n} t^i/i!); t(n,m) = Expansion(f(x,n)); t_out(n,m) = m!*t(n-m+1,m).

EXAMPLE

{1},

{1, 0},

{1, 0, -3},

{1, 0, 0, -4},

{1, 0, 0, -4, 25},

{1, 0, 0, 0, -5, 114},

{1, 0, 0, 0, -5, -6, -287},

{1, 0, 0, 0, 0, -6, 133, -4152},

{1, 0, 0, 0, 0, -6, -7, 552, -1647},

{1, 0, 0, 0, 0, 0, -7, -8,1629, 192230},

{1, 0, 0, 0, 0, 0, -7, -8, 621, -12610, 807961},

{1, 0, 0, 0, 0, 0, 0, -8, -9, 2510, -128579, -10164804},

{1, 0, 0, 0, 0, 0, 0, -8, -9, -10, 7381, -725484, -111209111},

{1, 0, 0, 0, 0,0, 0, 0, -9, -10, 2761, 18996, 1522651, 454840554},

{1, 0, 0, 0, 0, 0, 0,0, -9, -10, -11, 11076, -404989, 54082014, 14657978385}

MATHEMATICA

Clear[f, b, a, g, h, n, t]; f[t_, n_] = 1/(Exp[t] - Sum[t^i/i!, {i, 1, n}]); a = Table[Table[SeriesCoefficient[Series[f[t, m], {t, 0, 30}], n], {n, 0, 30}], {m, 1, 31}]; b = Table[Table[m!*a[[n - m + 1]][[m]], {m, 1, n }], {n, 1, 15}]; Flatten[b]

CROSSREFS

Cf. A089148.

Sequence in context: A054548 A059202 A244963 * A217334 A353859 A058865

Adjacent sequences:  A144449 A144450 A144451 * A144453 A144454 A144455

KEYWORD

uned,sign

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 06 2008

STATUS

approved

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Last modified June 29 18:25 EDT 2022. Contains 354913 sequences. (Running on oeis4.)