0,3

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

B. Berndt, Ramanujan's Notebooks, Part I, page 263.

A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 110.

T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. 2, Engelmann, Leipzig, 1880, p. 7.

J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.

T. D. Noe, Table of n, a(n) for n=0..50

Index entries for sequences related to factorial numbers

(-1)^(n-1)*a(n) is the coefficient of x^3 in prod(k=0, 2*n, x+2*k-2*n). - Benoit Cloitre and Michael Somos, Nov 22, 2002.

E.g.f.: (arcsin x)^4; that is, a_k is the coefficient of x^(2*k+2) in (arcsin x)^4 multiplied by (2*k+2)! and divided by 4! Also a(n) = 2^(2*n-2)*(n!)^2 * sum[ k=1..n ] k^(-2) - from Joe Keane (jgk(AT)jgk.org)

(arcsin x)^4 = x^4 + 2/3*x^6 + 7/15*x^8 + 328/945*x^10 + ...

(PARI) a(n)=if(n<0, 0, (2*n+2)!*polcoeff(asin(x+O(x^(2*n+3)))^4/4!, 2*n+2))

(PARI) a(n)=-(-1)^n*polcoeff(prod(k=0, 2*n, x+2*k-2*n), 3)

Cf. A001819, A001824, A001825, A049033.

Sequence in context: A034404 A012802 A049214 this_sequence A041763 A041760 A117798

Adjacent sequences: A002452 A002453 A002454 this_sequence A002456 A002457 A002458

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Joe Keane (jgk(AT)jgk.org)