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A104985 Row sums of triangle A104984. 2
1, 0, -2, -6, -20, -92, -554, -4002, -33096, -306440, -3135766, -35134670, -427878628, -5628940084, -79572364498, -1203168642362, -19379896959776, -331331041788640, -5993029816637262, -114348894263852326, -2295445815821635932, -48362099044178487564 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A104984 equals the matrix inverse of A104980.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..445

FORMULA

a(n) = Sum_{k=0..n} A104984(n, k).

MATHEMATICA

A003319[n_]:= A003319[n]= If[n==0, 0, n! -Sum[j!*A003319[n-j], {j, n-1}]];

A104984[n_, k_]:= If[k==n, 1, If[k==n-1, -n, -A003319[n-k]]];

a[n_]:= Sum[A104984[n, k], {k, 0, n}];

Table[a[n], {n, 0, 30}] (* G. C. Greubel, Jun 07 2021 *)

PROG

(PARI) {a(n)=sum(k=0, n, if(k==n, 1, if(k==n-1, -n, -polcoeff((1-1/sum(i=0, n-k, i!*x^i))/x+O(x^(n-k)), n-k-1) )))}

(Sage)

@CachedFunction

def T(n, k):

    if (k==n): return 1

    elif (k==n-1): return -n

    else: return -factorial(n-k) - sum( factorial(j)*T(n-k-j, 0) for j in (1..n-k-1) )

[sum(T(n, k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jun 07 2021

CROSSREFS

Cf. A104984, A104980.

Sequence in context: A005965 A000421 A009244 * A210690 A079575 A078564

Adjacent sequences:  A104982 A104983 A104984 * A104986 A104987 A104988

KEYWORD

sign

AUTHOR

Paul D. Hanna, Apr 10 2005

STATUS

approved

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Last modified September 24 15:58 EDT 2022. Contains 356943 sequences. (Running on oeis4.)