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 A046716 Coefficients of a special case of Poisson-Charlier polynomials. 15
 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; text; internal format)
 OFFSET 0,5 COMMENTS Diagonals: A000012, A000217; A000012, A002104. - Philippe Deléham, 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)!. - Philippe Deléham, Jun 18 2004 LINKS E. A. Enneking and J. C. Ahuja, Generalized Bell numbers, Fib. Quart., 14 (1976), 67-73. C. Radoux, Déterminants de Hankel et théorème de Sylvester, Séminaire Lotharingien de Combinatoire, B28b (1992), 9 pp. 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). - Philippe Deléham, 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). - Philippe Deléham, 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). EXAMPLE Triangle starts:   1;   1,  1;   1,  3,  1;   1,  6,  8,  1;   1, 10, 29, 24,  1;   ... 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 MATHEMATICA t[_, 0] = 1; t[n_, k_] := (-1)^k*Sum[(-1)^i*Binomial[n, i]*StirlingS1[i, n-k], {i, n-k, n}]; Table[t[n, k] // Abs, {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 10 2014 *) CROSSREFS Sequence in context: A056858 A137251 A158359 * A202605 A298636 A123354 Adjacent sequences:  A046713 A046714 A046715 * A046717 A046718 A046719 KEYWORD nonn,tabl,easy AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Jun 15 2004 STATUS approved

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Last modified August 9 10:10 EDT 2020. Contains 336323 sequences. (Running on oeis4.)