A191297 Expansion of exp(x^2*cos(x))=1+sum(n>0, a(n)*x^(2*n)/(2*n-2)!)

1, 1, 0, -7, -31, 1961, 33479, -2954291, -99285005, 13732118161, 626849624303, -147178659823339, -6633094420983493, 3009425456871930073, 78615467831373410599, -102564663540919291661795, 1659425702018862505784819, 5254049082422729980286018849, -472557550132644007343975782945, -370056978319441822040661209657819

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n)=(2*n-2)!*(sum(k=1..n-1, (2^(1-k)*(sum(i=0..floor((k-1)/2), (k-2*i)^(2*(n-k))*binomial(k,i)))*(-1)^(n-k))/(k!*(2*(n-k))!))+1/n!), n>0, a(0)=1.

Prog

(Maxima)
a(n):=(2*n-2)!*(sum((2^(1-k)*(sum((k-2*i)^(2*(n-k))*binomial(k, i), i, 0, floor((k-1)/2)))*(-1)^(n-k))/(k!*(2*(n-k))!), k, 1, n-1)+1/n!);

Crossrefs

Sequence in context: A197301 A280038 A253640 * A134709 A139314 A290969

Adjacent sequences: A191294 A191295 A191296 * A191298 A191299 A191300

Keyword

sign

Author

Vladimir Kruchinin, May 29 2011

Status

approved