A296769 Row sums of A296662.

1, 7, 38, 187, 874, 3958, 17548, 76627, 330818, 1415650, 6015316, 25413342, 106853668, 447472972, 1867450648, 7770342787, 32248174258, 133530264682, 551793690628, 2276098026922, 9373521044908, 38546133661492, 158301250009768, 649328801880622

Offset: 0

Author

Peter Luschny, Dec 20 2017

Keywords

• nonn

Crossrefs

Cf. A000531, A296662, bisection of A296663.

Programs

Maple

a := n -> 2^(1 + 2*n)*((2*GAMMA(5/2 + n))/(sqrt(Pi)*GAMMA(2 + n)) - 1):
seq(a(n), n=0..23);
# alternative
A296769 := proc(n)
    2^(2*n)*(doublefactorial(2*n+3)/(1+n)/doublefactorial(2*n)-2) ;
end proc:
seq(A296769(n),n=0..10) ; # R. J. Mathar, Jan 03 2018

Formula

a(n) = 2^(1 + 2*n)*((2*Gamma(5/2 + n))/(sqrt(Pi)*Gamma(2 + n)) - 1).

a(n) ~ 4^(n+1)*(sqrt(n/Pi) - 1/2).

a(n) = A000531(n+1). - R. J. Mathar, Jan 03 2018

a(n) = A033876(n)-2^(2*n+1). - R. J. Mathar, Jan 03 2018