A323322 G.f.: Sum_{n>=1} ( (1+x)^n + 2^n*x^n )^n / 2^n.

1, 7, 74, 1495, 43240, 1615922, 73898278, 3995605174, 249332639378, 17635891283696, 1394325697856104, 121850733104648549, 11663364820496833946, 1213527023075715931420, 136368036713803151862672, 16459661773011647036358779, 2123742016843422567243589246, 291703805646180153151632977150, 42495460119330209130801042623616, 6544578588779477399529020939623304

Offset

0,2

Links

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

Example

G.f.: A(x) = 1 + 7*x + 74*x^2 + 1495*x^3 + 43240*x^4 + 1615922*x^5 + 73898278*x^6 + 3995605174*x^7 + 249332639378*x^8 + 17635891283696*x^9 + ...
such that
A(x) = ((1+x) + 2*x)/2 + ((1+x)^2 + 2^2*x^2)^2/2^2 + ((1+x)^3 + 2^3*x^3)^3/2^3 + ((1+x)^4 + 2^4*x^4)^4/2^4 + ((1+x)^5 + 2^5*x^5)^5/2^5 + ((1+x)^6 + 2^6*x^6)^6/2^6 + ...

Prog

(PARI) \p120
{N = 25; Vec( round( sum(n=1, 500, ( (1+x +x*O(x^N))^n + 2^n*x^n )^n / 2^n *1.) ))}

Crossrefs

Sequence in context: A097821 A337387 A054745 * A356589 A326221 A197091

Adjacent sequences: A323319 A323320 A323321 * A323323 A323324 A323325

Keyword

nonn

Author

Paul D. Hanna, Jan 10 2019

Status

approved