A326556 E.g.f. C(x)^2 = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!^2, where C(x) = cos( Integral 1/x * (Integral C(x) dx) dx ) is the e.g.f of A326551.

1, -4, 256, -67072, 49479680, -82817122304, 273099601739776, -1606512897507196928, 15659025634284911198208, -238894370882781809622384640, 5451274531297360096585324691456, -179296966081016547805899589056200704, 8242844472527700570663352676068232265728, -516102091343047279882754030489835708929277952, 43042816831864259208854418353099287467922680709120

Offset

0,2

Comments

The e.g.f. C(x)^2 can be derived from the functions described by A326800, A326801, and A326802.

Links

Table of n, a(n) for n=0..14.

Example

E.g.f.: C(x)^2 = 1 - 4*x^2/2!^2 + 256*x^4/4!^2 - 67072*x^6/6!^2 + 49479680*x^8/8!^2 - 82817122304*x^10/10!^2 + 273099601739776*x^12/12!^2 - 1606512897507196928*x^14/14!^2 + 15659025634284911198208*x^16/16!^2 - 238894370882781809622384640*x^18/18!^2 + 5451274531297360096585324691456*x^20/20!^2 + ...
where C(x) is the e.g.f. of A326551:
C(x) = 1 - 2*x^2/2!^2 + 56*x^4/4!^2 - 8336*x^6/6!^2 + 3985792*x^8/8!^2 - 4679517952*x^10/10!^2 + 11427218287616*x^12/12!^2 - 51793067942397952*x^14/14!^2 + 400951893341645930496*x^16/16!^2 - 4975999084909976839454720*x^18/18!^2 + 94178912073481319162642169856*x^20/20!^2 -+ ...
such that C(x) = cos( Integral 1/x * (Integral C(x) dx) dx ),
note also C(x*y) = cos( Integral Integral C(x*y) dx dy ).

Prog

(PARI)
{a(n) = my(C=1, S=x); for(i=1, 2*n,
S = intformal( C/x * intformal( C +x*O(x^(2*n)) ) );
C = 1 - intformal( S/x * intformal( C +x*O(x^(2*n)) ) ); ); (2*n)!^2*polcoeff(C^2, 2*n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A326551, A326800, A326801, A326802.

Sequence in context: A223755 A223844 A122249 * A223795 A207275 A207473

Adjacent sequences: A326553 A326554 A326555 * A326557 A326558 A326559

Keyword

sign

Author

Paul D. Hanna, Jul 28 2019

Status

approved