A027182 a(n) = self-convolution of row n of array T given by A027170.

18, 150, 820, 3726, 15492, 61660, 240328, 928110, 3572692, 13749580, 52977216, 204478276, 790747504, 3063728856, 11891504944, 46231328174, 180005765748, 701823431740, 2739725128448, 10707198384348, 41888225645152, 164027934617024

Offset

1,1

Comments

Let g(x) = Sum_(k=0..n) A027170(n,k)*x^k be the generating function of row n, then a(n) = [x^n] g(x)^2. - R. J. Mathar, May 06 2026

Links

Table of n, a(n) for n=1..22.

Formula

Conjecture: D-finite with recurrence 2*(n+2)*a(n) +(-17*n-23)*a(n-1) +(47*n+36)*a(n-2) +2*(-22*n-17)*a(n-3) +4*(-n+20)*a(n-4) +8*(2*n-9)*a(n-5) +24*(12*n-47)=0. - R. J. Mathar, May 06 2026

Example

a(2) = 5*5+10*10+5*5=120. a(3) = 7*7+19*19+19*19+7*7=820. - R. J. Mathar, May 06 2026

Maple

A027182 := proc(n)
    local x, k ;
    add(A027170(n, k)*x^k, k=0..n) ;
    %^2 ;
    coeff(%, x^n) ;
end proc:
seq(A027182(n), n=1..40) ;

Crossrefs

Cf. A027170.

Sequence in context: A221352 A271755 A197214 * A294486 A228994 A235397

Adjacent sequences: A027179 A027180 A027181 * A027183 A027184 A027185

Keyword

nonn

Author

Clark Kimberling

Extensions

Offset corrected. - R. J. Mathar, May 06 2026

Status

approved