A380975 Self-convolution of A300116.

1, 80, 5616, 378880, 25108976, 1647924480, 107513168896, 6986714808320, 452774526525936, 29282607270465280, 1890903981075228416, 121957594044379545600, 7858392761937306551296, 505967049989822738186240, 32556176323125901615005696, 2093691733876474661699584000

Offset: 0

Author

Vaclav Kotesovec, Feb 10 2025, following a suggestion from John M. Campbell

Keywords

• nonn

Crossrefs

Cf. A300116.

Programs

Mathematica

RecurrenceTable[{-262144*(n-1)^5*a[n-3] + 512*(-10 + 53*n - 115*n^2 + 130*n^3 - 80*n^4 + 24*n^5)*a[n-2] - 8*(-2 + 13*n - 35*n^2 + 50*n^3 - 40*n^4 + 24*n^5)*a[n-1] + n^5*a[n] == 0, a[0] == 1, a[1] == 80, a[2] == 5616}, a, {n, 0, 20}]

Formula

Recurrence: n^5*a(n) = 8*(24*n^5 - 40*n^4 + 50*n^3 - 35*n^2 + 13*n - 2)*a(n-1) - 512*(24*n^5 - 80*n^4 + 130*n^3 - 115*n^2 + 53*n - 10)*a(n-2) + 262144*(n-1)^5*a(n-3).

a(n) ~ Gamma(1/4)^8 * 2^(6*n - 4) / Pi^6.