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A046716
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Coefficients of a special case of Poisson-Charlier polynomials.
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14
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1, 1, 1, 1, 3, 1, 1, 6, 8, 1, 1, 10, 29, 24, 1, 1, 15, 75, 145, 89, 1, 1, 21, 160, 545, 814, 415, 1, 1, 28, 301, 1575, 4179, 5243, 2372, 1, 1, 36, 518, 3836, 15659, 34860, 38618, 16072, 1, 1, 45, 834, 8274, 47775, 163191, 318926, 321690, 125673, 1, 1, 55, 1275, 16290
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Diagonals : A000012, A000217; A000012, A002104 - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jun 12 2004
The sequence a(n) = Sum_{k = 0..n} T(n,k)*x^(n-k) is the binomial transform of the sequence b(n) = (n+x-1)! / (x-1)! . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jun 18 2004
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REFERENCES
| E. A. Enneking and J. C. Ahuja, Generalized Bell numbers, Fib. Quart., 14 (1976), 67-73.
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LINKS
| C. Radoux, Determinants de Hankel et theoreme de Sylvester
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FORMULA
| Reference gives a recurrence.
Sum_{k = 0..n} T(n, k)*x^(n-k) = A000522(n), A001339(n), A082030(n) for x = 1, 2, 3 respectively . Sum_{k = 0..n} T(n, k)*2^k = A081367(n) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jun 12 2004
Let P(x, n) = Sum_{k = 0..n} T(n, k)*x^k, then Sum_{n>=0} P(x, n)*t^n / n! = exp(xt)/(1-xt)^(1/x) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jun 12 2004
T(n, 0) = 1, T(n, k) = (-1)^k * Sum[i=n-k..n, (-1)^i*C(n, i)*S1(i, n-k)], where S1 = Stirling numbers of first kind (A008275).
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EXAMPLE
| 1; 1,1; 1,3,1; 1,6,8,1; 1,10,29,24,1; ...
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MAPLE
| a := proc(n, k) option remember;
if k = 0 then 1
elif k < 0 then 0
elif k = n then (-1)^n
else a(n-1, k) - n*a(n-1, k-1) - (n-1)*a(n-2, k-2) fi end:
A046716 := (n, k) -> abs(a(n, k));
seq(seq(A046716(n, k), k=0..n), n=0..9); - Peter Luschny, Apr 05 2011
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CROSSREFS
| Sequence in context: A056858 A137251 A158359 * A202605 A123354 A120247
Adjacent sequences: A046713 A046714 A046715 * A046717 A046718 A046719
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 15 2004
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