A397062 Self-convolution of A305102.

0, 0, 1, 8, 36, 126, 376, 1004, 2469, 5688, 12434, 26012, 52428, 102326, 194180, 359436, 650740, 1154850, 2012765, 3450684, 5827214, 9704648, 15955728, 25922184, 41648520, 66224182, 104281142, 162712832, 251706732, 386218990, 588069016, 888899176, 1334336593, 1989817604, 2948702406

Offset

0,4

Links

Table of n, a(n) for n=0..34.

Formula

G.f.: (Sum_{k>=1} x^k/(1-x^k) * Product_{k>=1} (1+x^k)/(1-x^k))^2.

a(n) ~ exp(Pi*sqrt(2*n)) * (log(2*n/Pi^2) + 2*gamma)^2 / (2^(19/4) * Pi^2 * n^(1/4)), where gamma is the Euler-Mascheroni constant A001620.

Mathematica

nmax = 50; CoefficientList[Series[(Sum[x^k/(1-x^k), {k, 1, nmax}] * Product[(1+x^k)/(1-x^k), {k, 1, nmax}])^2, {x, 0, nmax}], x]

Crossrefs

Cf. A006128, A305082, A305102.

Cf. A305120, A397061.

Sequence in context: A347751 A341222 A213581 * A276279 A210379 A131123

Adjacent sequences: A397059 A397060 A397061 * A397063 A397065 A397067

Keyword

nonn

Author

Vaclav Kotesovec, Jun 15 2026

Status

approved