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A091885
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Triangle T(n,k) defined by the generating function cosh(sqrt(y)*arcsin(x)) + sqrt(y)*sinh(sqrt(y)*arcsin(x))-1 = sum(n>=1, sum(k=1..n, T(n,k)*y^k) *x^n/n! ).
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2
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1, 1, 1, 1, 4, 1, 9, 10, 1, 64, 20, 1, 225, 259, 35, 1, 2304, 784, 56, 1, 11025, 12916, 1974, 84, 1, 147456, 52480, 4368, 120, 1, 893025, 1057221, 172810, 8778, 165, 1, 14745600, 5395456, 489280, 16368, 220, 1, 108056025, 128816766, 21967231, 1234948, 28743
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Row sums are equal to A006228(n). This is sequence A121408 without the intertwining zeros. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 28 2006
This number triangle corresponds to the coefficients of the polynomial of the denominator of Fourier cosine coefficients for functions of the form sin(x)^(2*k) for integer n. For example (k=5), evaluating Integrate(cos(n*x)*sin(x)^10,{x,-Pi,Pi}), we have -((7257600*sin(n*Pi)))/(-14745600*n + 5395456*n^3 - 489280*n^5 + 16368*n^7 - 220*n^9 + n^11)); note the sequence of the coefficients of the polynomial of the denominator: -14745600, 5395456, -489280, 16368, -220, 1. [From John M. Campbell (jmaxwellcampbell(AT)gmail.com), May 28, 2011]
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EXAMPLE
| Triangle starts:
1;
1;
1,1;
4,1;
9,10,1;
64,20,1;
225,259,35,1;
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MAPLE
| G:=cosh(sqrt(y)*arcsin(x))+sqrt(y)*sinh(sqrt(y)*arcsin(x))-1: Gser:=simplify(series(G, x=0, 15)): for n from 1 to 13 do P[n]:=sort(expand(n!*coeff(Gser, x, n))) od: for n from 1 to 13 do seq(coeff(P[n], y, k), k=1..ceil(n/2)) od; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 28 2006
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CROSSREFS
| Cf. A006228.
Cf. A121408.
Sequence in context: A084887 A067015 A158199 * A069606 A193580 A075150
Adjacent sequences: A091882 A091883 A091884 * A091886 A091887 A091888
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KEYWORD
| nonn,tabf,easy
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AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Feb 08 2004
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EXTENSIONS
| More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
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